Differential Geometry

Victor V. Prasolov, Olga Sipacheva

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Russian

Springer Nature Switzerland AG
11 February 2022

Differential & Riemannian geometry

Series: Moscow Lectures

This book combines the classical and contemporary approaches to differential geometry. An introduction to the Riemannian geometry of manifolds is preceded by a detailed discussion of properties of curves and surfaces.

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.

By: Victor V. Prasolov
Translated by: Olga Sipacheva
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 2022 ed.
Volume: 8
Dimensions: Height: 235mm, Width: 155mm,
Weight: 594g
ISBN: 9783030922481
ISBN 10: 3030922480
Series: Moscow Lectures
Pages: 271
Publication Date: 11 February 2022
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Curves in the Plane.- Curves in Space.- Surfaces in Space.- Hypersurfaces in Rn+1.- Connections.- Riemannian Manifolds.- Lie Groups.- Comparison Theorems.- Curvature and Topology.- Laplacian.- Appendix.- Bibliography.- Index.

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).

Reviews for Differential Geometry

All chapters are supplemented with solutions of the problems scattered throughout the text. Designed as a text for a lecturer course on the subject, it is perfect and can be recommended for students interested in this classical field. (Ivailo. M. Mladenov, zbMATH 1498.53001, 2022)