Skip to content
Register Sign in Wishlist
Lectures on Kähler Geometry

Lectures on Kähler Geometry

$150.00 (P)

Part of London Mathematical Society Student Texts

  • Date Published: May 2007
  • availability: Available
  • format: Hardback
  • isbn: 9780521868914

$ 150.00 (P)
Hardback

Add to cart Add to wishlist

Other available formats:
Paperback, eBook


Looking for an examination copy?

If you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact collegesales@cambridge.org providing details of the course you are teaching.

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi–Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.

    • The first graduate-level text on Kähler geometry, providing a concise introduction for both mathematicians and physicists with a basic knowledge of calculus in several variables and linear algebra
    • Over 130 exercises and worked examples
    • Self-contained and presents varying viewpoints including Riemannian, complex and algebraic
    Read more

    Reviews & endorsements

    "A concise and well-written modern introduction to the subject."
    Tatyana E. Foth, Mathematical Reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: May 2007
    • format: Hardback
    • isbn: 9780521868914
    • length: 182 pages
    • dimensions: 229 x 152 x 14 mm
    • weight: 0.44kg
    • contains: 131 exercises
    • availability: Available
  • Table of Contents

    Introduction
    Part I. Basics on Differential Geometry:
    1. Smooth manifolds
    2. Tensor fields on smooth manifolds
    3. The exterior derivative
    4. Principal and vector bundles
    5. Connections
    6. Riemannian manifolds
    Part II. Complex and Hermitian Geometry:
    7. Complex structures and holomorphic maps
    8. Holomorphic forms and vector fields
    9. Complex and holomorphic vector bundles
    10. Hermitian bundles
    11. Hermitian and Kähler metrics
    12. The curvature tensor of Kähler manifolds
    13. Examples of Kähler metrics
    14. Natural operators on Riemannian and Kähler manifolds
    15. Hodge and Dolbeault theory
    Part III. Topics on Compact Kähler Manifolds:
    16. Chern classes
    17. The Ricci form of Kähler manifolds
    18. The Calabi–Yau theorem
    19. Kähler–Einstein metrics
    20. Weitzenböck techniques
    21. The Hirzebruch–Riemann–Roch formula
    22. Further vanishing results
    23. Ricci–flat Kähler metrics
    24. Explicit examples of Calabi–Yau manifolds
    Bibliography
    Index.

  • Author

    Andrei Moroianu, Ecole Polytechnique, Paris
    Andrei Moroianu is a Researcher at CNRS and a Professor of Mathematics at Ecole Polytechnique.

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×