Prasolov V. Differential Geometry 2022 torrent

Textbook in PDF format

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.\
Curves in the Plane
Curves in Space
Surfaces in Space
Hypersurfaces in Rn+1: Connections
Riemannian Manifolds
Lie Groups
Comparison Theorems, Curvature and Topology, and Laplacian
Appendix