Oliver Yau Popular Books
Oliver Yau Biography & Facts
In algebraic and differential geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics. Particularly in superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to the idea of mirror symmetry. Their name was coined by Candelas et al. (1985), after Eugenio Calabi (1954, 1957) who first conjectured that such surfaces might exist, and Shing-Tung Yau (1978) who proved the Calabi conjecture. Calabi–Yau manifolds are complex manifolds that are generalizations of K3 surfaces in any number of complex dimensions (i.e. any even number of real dimensions). They were originally defined as compact Kähler manifolds with a vanishing first Chern class and a Ricci-flat metric, though many other similar but inequivalent definitions are sometimes used. Definitions The motivational definition given by Shing-Tung Yau is of a compact Kähler manifold with a vanishing first Chern class, that is also Ricci flat. There are many other definitions of a Calabi–Yau manifold used by different authors, some inequivalent. This section summarizes some of the more common definitions and the relations between them. A Calabi–Yau n {\displaystyle n} -fold or Calabi–Yau manifold of (complex) dimension n {\displaystyle n} is sometimes defined as a compact n {\displaystyle n} -dimensional Kähler manifold M {\displaystyle M} satisfying one of the following equivalent conditions: The canonical bundle of M {\displaystyle M} is trivial. M {\displaystyle M} has a holomorphic n {\displaystyle n} -form that vanishes nowhere. The structure group of the tangent bundle of M {\displaystyle M} can be reduced from U ( n ) {\displaystyle U(n)} , the unitary group, to S U ( n ) {\displaystyle SU(n)} , the special unitary group. M {\displaystyle M} has a Kähler metric with global holonomy contained in S U ( n ) {\displaystyle SU(n)} . These conditions imply that the first integral Chern class c 1 ( M ) {\displaystyle c_{1}(M)} of M {\displaystyle M} vanishes. Nevertheless, the converse is not true. The simplest examples where this happens are hyperelliptic surfaces, finite quotients of a complex torus of complex dimension 2, which have vanishing first integral Chern class but non-trivial canonical bundle. For a compact n {\displaystyle n} -dimensional Kähler manifold M {\displaystyle M} the following conditions are equivalent to each other, but are weaker than the conditions above, though they are sometimes used as the definition of a Calabi–Yau manifold: M {\displaystyle M} has vanishing first real Chern class. M {\displaystyle M} has a Kähler metric with vanishing Ricci curvature. M {\displaystyle M} has a Kähler metric with local holonomy contained in S U ( n ) {\displaystyle SU(n)} . A positive power of the canonical bundle of M {\displaystyle M} is trivial. M {\displaystyle M} has a finite cover that has trivial canonical bundle. M {\displaystyle M} has a finite cover that is a product of a torus and a simply connected manifold with trivial canonical bundle. If a compact Kähler manifold is simply connected, then the weak definition above is equivalent to the stronger definition. Enriques surfaces give examples of complex manifolds that have Ricci-flat metrics, but their canonical bundles are not trivial, so they are Calabi–Yau manifolds according to the second but not the first definition above. On the other hand, their double covers are Calabi–Yau manifolds for both definitions (in fact, K3 surfaces). By far the hardest part of proving the equivalences between the various properties above is proving the existence of Ricci-flat metrics. This follows from Yau's proof of the Calabi conjecture, which implies that a compact Kähler manifold with a vanishing first real Chern class has a Kähler metric in the same class with vanishing Ricci curvature. (The class of a Kähler metric is the cohomology class of its associated 2-form.) Calabi showed such a metric is unique. There are many other inequivalent definitions of Calabi–Yau manifolds that are sometimes used, which differ in the following ways (among others): The first Chern class may vanish as an integral class or as a real class. Most definitions assert that Calabi–Yau manifolds are compact, but some allow them to be non-compact. In the generalization to non-compact manifolds, the difference ( Ω ∧ Ω ¯ − ω n / n ! ) {\displaystyle (\Omega \wedge {\bar {\Omega }}-\omega ^{n}/n!)} must vanish asymptotically. Here, ω {\displaystyle \omega } is the Kähler form associated with the Kähler metric, g {\displaystyle g} . Some definitions put restrictions on the fundamental group of a Calabi–Yau manifold, such as demanding that it be finite or trivial. Any Calabi–Yau manifold has a finite cover that is the product of a torus and a simply-connected Calabi–Yau manifold. Some definitions require that the holonomy be exactly equal to S U ( n ) {\displaystyle SU(n)} rather than a subgroup of it, which implies that the Hodge numbers h i , 0 {\displaystyle h^{i,0}} vanish for 0 < i .... Discover the Oliver Yau popular books. Find the top 100 most popular Oliver Yau books.
Best Seller Oliver Yau Books of 2024
-
Always Yours
Claire RayeSome things are just meant to be... Ellen Somerville and Will McIntyre met by accident and under unusual circumstances. Getting sprayed by a skunk in a parking lot wouldn’t normall...
-
Eternal
W.J. MayShe will fight for what is hers. When the king is murdered, Katerina, his only daughter, must flee for her life. She finds herself on a strange and dangerous path. Alone for the fi...
-
The Adventures of Sherlock Holmes
Arthur Conan DoyleAn Apple Books Classic You get not one, not two, but 25 gripping mysteries in Arthur Conan Doyle’s first of five collections of Sherlock Holmes short stories. Follow the brilliant ...
-
Get Lucky
Lila MonroeFall for the hot and hilarious romcom spin on 'The Hangover', perfect for fans of Tessa Bailey, Ali Hazelwood, and Emily Henry! What happens when you wake up in a hotel s...
-
The Cupcake Cottage
Jean OramNHL player Maverick Blades could fall in love with anyone... But he had to fall for a woman who falls under the Bro Code as untouchablehis best friend’s beautiful ex, DaisyMae Ray....
-
Hard Love
Peyton BanksHe was football royalty. Legendary quarterback. A champion.  Reiner Strickland had led his team to three national championships and playing a knight in shining armor was a...
-
Never Enough
Lexy TimmsBe good enough never is... Anthony Accardi is a man on a mission: make his father's watch company a success while bringing in millions of dollars. To do that, he needs an assi...
-
Meditations
Emperor of Rome Marcus AureliusMeditations is a series of personal writings by Marcus Aurelius, Roman Emperor 161–180 CE, setting forth his ideas on Stoic philosophy.
-
Salvation
Meghan O'FlynnIf you like mouthy detectives, serial killers, and suspenseful mysteries that don't quit, this chilling and actionpacked hardboiled detective series has you covered! Try this ...
-
Becoming Lady Dalton
Carrie LomaxA dance of desire and deceit... In the glittering world of London's ton, Mrs. Viola Cartwright revels in her newfound freedom as a lady of leisureuntil a series of jewel theft...
-
All Fired Up
Kathryn ShayCaptain Jarek Zenko, a war veteran and firefighter, meets Lacey Roth at a bar one night. They don’t share their real identities, even when they retreat to a hotel. When they meet t...
-
His Girl Next Door
Khardine GrayFrom USA Today Bestselling author Khardine Gray comes a sizzling hot single dad romance you won't want to miss. No strings attached fun with the ubergorgeous single d...
-
How to Choose a Guy in 10 Days
Lila MonroeThe only thing more hilarious than the movies is… real life?! Fall in love with the sizzling grumpysunshine romantic comedy perfect for fans of Sophie Kinsella and Ali Hazlewood! ...
-
Death at Hazel House
Betty Rowlands‘Riveting, can't put it down! I love this story… a wonderfully twisted tale of a crime that has more twists than I thought possible... fantastic.’ Goodreads Reviewer, 5 stars ...
-
Dracula
Bram StokerAn Apple Books Classic edition. Few characters have seized readers’ imaginations quite like Count Dracula of Transylvania, the hero of Bram Stoker’s classic. The 1897 novel put vam...
-
Nothing to Hide
Scarlett FinnPrize of a lifetime: travel the world with a celebrity billionaire. Come to LA with us, Roxie… It will be so much fun! We have tickets for a latenight talk show! What could possibl...
-
A Bookshop to Die For
M.P. BlackDitching her fiancé at the altar, Alice Hartford bolts to her childhood hometown to reconnect with the last, happy remnant of her past: her mom's old bookstore. But the bookst...
-
Caught Up with the Captain
Kait NolanCan a retired naval commander and the love he left behind overcome a 34yearold secret to find their way to a second chance? Captain Mitchell Greyson is a man who believes in duty. ...
-
The Holy Bible - King James Version
King JamesHoly Bible King James Version Few Sample Paragraphs from The Holy Bible eBook, Genesis (OT) 1 Gen. 1 IN the beginning God created the heaven and the earth. 2 And the earth was with...
-
Pride and Prejudice
Jane AustenAn Apple Books Classic edition. Jane Austen’s beloved classic opens with this witty and very memorable line: “It is a truth universally acknowledged, that a single man in possessio...
-
Inception of Gold
Lexy TimmsThings are not as bad as they seem. They are worse. Being the personal assistant to a narcissistic actress who just happens to own the key to my family's undoing isn't ex...
-
Wuthering Heights
Emily BrontëAn Apple Books Classic edition. If you’ve only ever seen Wuthering Heights on screen, you may have an image of Catherine and Heathcliff as the ultimate starcrossed lovers. But that...
-
Silenced Girls
Roger Stelljes“ Wow wow wow!  Grips you in a choke hold and  does not let go … Oozes suspense and  bonechilling twists and turns .  Astonishing … One of those...
-
Hot Off the Press
Lexy Timms"This is what really happened… reported by a free press, for a free people…" Wes Shaw leads a secret double life. As the secret owner of a billion dollar newspap...
-
The Target
Lexy TimmsWhen you seek revenge be sure to dig two graves… Revenge was the only thing I had going for me. It kept me awake at night and drove me into desperate situations in dive bars across...
-
Awaken Me
Jenna JacobHe was more than a ghost haunting my dreams…he was real. By day, I’m Julianna Garrett …a prim, proper accountant. By night, I’m tormented by dreams of an alpha, ambereyed Adonis wh...
-
Noxious
Lexy TimmsStop setting yourself on fire to keep someone else warm. Brady and Levi have been together since high school, since before he became famous and started thinking only about himself....
-
Dark Psychology and Manipulation
Margaret MorrisonTHE MENTAL MANIPULATOR WILL NO LONGER KEEP SECRETS FROM YOU! Are you fed up with the wool being pulled over your eyes?Are you prepared to stand up to those who believe they can man...
-
School of Potential
W.J. MayUSA Today Bestselling author, W.J. May brings you a continuation of the international bestselling series, The Chronicles of Kerrigan! Come back and enjoy the famous characters, or ...
-
Think and Grow Rich
Greg Habstritt & Napoleon HillThink and Grow Rich is one of the most popular success book of alltime, having sold more than 60 million copies since it was first published more than 70...
-
The Great Gatsby
F. Scott FitzgeraldAn Apple Books Classics edition. The Roaring Twenties are in full effect in F. Scott Fitzgerald’s riveting classic. Manabouttown Jay Gatsby seems to have it all, including loads of...
-
A Green Kind of Witch
Sierra CrossCinderella crossed with Mean Girls.   That's what Hazel's daily existence feels like. Born to a family of elegant yet shallow Beige Witches, seventeen y...
-
Law of Attraction
Jordan HollisHow to Finally Overcome the Hurdles of Manifesting Proven, effective and enjoyable ways to help you manifest faster… Right now, think of something that makes you successful. If you...
-
Assisting the Bosshole
Kristin MacQueenNo hot water? Check Missed the train? Check Broke my heel? Check Dropped my coffee? Check My first day of my new job can’t possibly go worse, right? Wrong. When I meet Parker Scott...
-
Tempting the King
Jessa YorkAn escaped Mafia Queen, hiding from her past. A Mafia King who wants to claim her… Giselle They think I'm lostbut I know better. I can never be found. The path I've creat...
-
Peace on Earth
Maia RossCrime never takes a holiday. Why should Irma? Irma Abercrombie is an energetic retiree with a shadowy past, a mean right hook, and a profound love of Christmas. Surrounded by seaso...
-
The Stoic Mind
Addy Osmani & GoLimitlesssDiscover the timeless wisdom of Stoicism in a modern context with "The Stoic Mind," an enlightening visual guide by Addy Osmani and GoLimitlesss. This rich exploration co...
-
The Wonderful Wizard of Oz
L. Frank BaumAn Apple Books Classic edition. You’ve seen the iconic 1939 movie, but do you know about the talking field mice, the Winkies, and the Witch of the North that appear in the original...
-
Pretty Little Lies
Ivy ThornFour years ago, Nicolo Marchetti took my innocence. But he left me with something else Nicolo almost took everything from me. My virginity, my reputation, and very nearly my future...
-
Christmas in Sweetbriar Cove
Melody GraceCelebrate the holidays in Sweetbriar Cove with this festive romance collection, containing two sizzling smalltown holiday stories perfect for fans of Tessa Bailey, Sophie Kinsella...
-
The Next Girl
Carla KovachIF YOU ONLY READ ONE BOOK THIS YEAR, MAKE IT THE NEXT GIRL... You thought he’d come to save you. You were wrong. ‘ Absolutely the best thriller I’ve read this year! ’ Goodreads Rev...
-
Whiskey Girl
Melissa BelleThey'll do anything for each other…except commit. Logan Wild isn’t just the hottest broncriding cowboy in Texas. He’s also my best friendwith benefits. And that’s all we’ll ev...
-
Alpha
Sybil BartelBillionaire. Mercenary. Navy SEAL. The Teams trained me to be a killer. War taught me to be ruthless. Then an illfated mission proved I was human. Combat wounded, cut loose by the ...
-
Little Women
Louisa May AlcottAn Apple Books Classic edition. Meet the Marches! Louisa May Alcott’s classic introduces us to four unforgettable sisters: beautiful Meg, tomboyish Jo, delicate Beth, and Amy, the ...
-
The Icing on the Cake
Linda SeedShe’s a baker without a kitchen. He’s got a double oven to spare. It’s a recipe for success, until his mother starts stirring up trouble … Cassie Jordan has a sweet dream to open a...
-
Man In The Water
Jon HillAn attempted murder. A missing spouse. And an international conspiracy that could change the world. Jack Green has always been skeptical of socalled facts. Though he's forced ...
-
A Christmas Carol
Charles DickensAn Apple Books Classic edition. It’s Christmas Eve in Victorian England. While some families don’t know where their next meal will come from, Ebenezer Scrooge sits in his large hom...
-
Masters of Restraint
Ines JohnsonMy new boss is good at giving orders. But his latest demand is NSFW. Especially when his two business partners want in on our deal. My new boss My boss’s boss Their investor &#...
-
His Own Heaven
Jennie KewWinner of the 2021 Passionate Plume Award for BDSM Romance Finalist in the 2021 Stiletto Contest for Contemporary Romance He taught her to trust, she taught him to love. Lucy Bar...
-
The Three Little Pigs
Mark LeskyClassic fairy tales, legends and folk stories in short version without violence retold with lovely illustrations in simple language. Perfect for reading aloud to small chi...