Skip to content
Register Sign in Wishlist
Projective Differential Geometry Old and New

Projective Differential Geometry Old and New
From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups

£97.99

Part of Cambridge Tracts in Mathematics

  • Date Published: January 2005
  • availability: Available
  • format: Hardback
  • isbn: 9780521831864

£ 97.99
Hardback

Add to cart Add to wishlist

Other available formats:
eBook


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and mathematical physics. They also give results and proofs of classic theorems. Exercises play a prominent role: historical and cultural comments set the basic notions in a broader context. The book opens by discussing the Schwarzian derivative and its connection to the Virasoro algebra. One-dimensional projective differential geometry features strongly. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, and the classical four-vertex theorem. The classical theory of projective hypersurfaces is surveyed and related to some very recent results and conjectures. A final chapter considers various versions of multi-dimensional Schwarzian derivative. In sum, here is a rapid route for graduate students and researchers to the frontiers of current research in this evergreen subject.

    • Presents and summarizes recent research scattered in mathematical journals, and features historical, cultural and bibliographical comments collected at the end of each section
    • Numerous exercises help the reader to master basic techniques and make it possible to avoid lengthy computation in the text of the book
    • A unique feature of this book is that it puts classical projective differential geometry into a broader mathematical context and connects it with contemporary mathematics and mathematical physics
    Read more

    Reviews & endorsements

    '… this is an introduction to global projective differential geometry offering felicitous choice of topics, leading from classical projective differential geometry to current fields of research in mathematics and mathematical physics. The reader is guided from simple facts concerning curves and derivatives to more involved problems and methods through a world of inspiring ideas, delivering insights in deep relations. Historical comments as well as stimulating exercises occur frequently throughout the text, making it suitable for teachings.' Zentralblatt MATH

    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: January 2005
    • format: Hardback
    • isbn: 9780521831864
    • length: 262 pages
    • dimensions: 229 x 152 x 19 mm
    • weight: 0.56kg
    • contains: 53 b/w illus. 35 exercises
    • availability: Available
  • Table of Contents

    Preface: why projective?
    1. Introduction
    2. The geometry of the projective line
    3. The algebra of the projective line and cohomology of Diff(S1)
    4. Vertices of projective curves
    5. Projective invariants of submanifolds
    6. Projective structures on smooth manifolds
    7. Multi-dimensional Schwarzian derivatives and differential operators
    Appendix 1. Five proofs of the Sturm theorem
    Appendix 2. The language of symplectic and contact geometry
    Appendix 3. The language of connections
    Appendix 4. The language of homological algebra
    Appendix 5. Remarkable cocycles on groups of diffeomorphisms
    Appendix 6. The Godbillon–Vey class
    Appendix 7. The Adler–Gelfand–Dickey bracket and infinite-dimensional Poisson geometry
    Bibliography
    Index.

  • Authors

    V. Ovsienko, Université Lyon I

    S. Tabachnikov, Pennsylvania State University

related links

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.
×