微分幾何学（テキスト） Differential Geometry (Moscow Lectures)

Prasolov, Victor V./ Sipacheva, Olga (TRN)

Springer Nature Switzerland AG（2022/02発売）

Springer Nature Switzerland AG（2022/02発売）

• 製本 Hardcover:ハードカバー版／ページ数 271 p.
• 言語 ENG
• 商品コード 9783030922481

Full Description

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.

Contents

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.