Overview
- Combines the classical and contemporary approaches to differential geometry
- Detailed discussion of properties of curves and surfaces
- Various approaches to Gaussian curvature for surfaces are discussed
Part of the book series: Moscow Lectures (ML, volume 8)
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Table of contents (8 chapters)
Keywords
About this book
The chapter on the differential geometry of plane curves considers local and global properties of curves, evolutes and involutes, and affine and projective differential geometry. Various approaches to Gaussian curvature for surfaces are discussed. The curvature tensor, conjugate points, and the Laplace-Beltrami operator are first considered in detail for two-dimensional surfaces, which facilitates studying them in the many-dimensional case. A separate chapter is devoted to the differential geometry of Lie groups.
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Authors and Affiliations
About the author
Victor Prasolov, born 1956, is a permanent teacher of mathematics at the Independent University of Moscow. He published two books with Springer, Polynomials and Algebraic Curves. Towards Moduli Spaces (jointly with M. E. Kazaryan and S. K. Lando) and eight books with AMS, including Problems and Theorems in Linear Algebra, Intuitive Topology, Knots, Links, Braids, and 3-Manifolds (jointly with A. B. Sossinsky), and Elliptic Functions and Elliptic Integrals (jointly with Yu. Solovyev).
Bibliographic Information
Book Title: Differential Geometry
Authors: Victor V. Prasolov
Translated by: Olga Sipacheva
Series Title: Moscow Lectures
DOI: https://doi.org/10.1007/978-3-030-92249-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-030-92248-1Published: 11 February 2022
Softcover ISBN: 978-3-030-92251-1Published: 11 February 2023
eBook ISBN: 978-3-030-92249-8Published: 10 February 2022
Series ISSN: 2522-0314
Series E-ISSN: 2522-0322
Edition Number: 1
Number of Pages: XI, 271
Number of Illustrations: 1 b/w illustrations
Topics: Differential Geometry