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Differential geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	Differential geometryby Victor V. Prasolov.
Author:	Prasolov, Victor V.
Published:	Cham :Springer International Publishing :2022.
Description:	xi, 271 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Geometry, Differential.
Online resource:	https://doi.org/10.1007/978-3-030-92249-8
ISBN:	9783030922498$q(electronic bk.)

Differential geometry
Prasolov, Victor V.

Differential geometry[electronic resource] /by Victor V. Prasolov. - Cham :Springer International Publishing :2022. - xi, 271 p. :ill., digital ;24 cm. - Moscow lectures,v. 82522-0322 ;. - Moscow lectures ;v.1..

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.

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.

ISBN: 9783030922498$q(electronic bk.)

Standard No.: 10.1007/978-3-030-92249-8doiSubjects--Topical Terms:

182610
Geometry, Differential.

LC Class. No.: QA641 / .P73 2022

Dewey Class. No.: 516.36

Differential geometry
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520 $a 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.
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