(Ebook) Differential Geometry by Victor V. Prasolov; Olga Sipacheva (Translator) ISBN 9783030922481, 3030922480, B09S9VJN63

(Ebook) Differential Geometry by Victor V. Prasolov; Olga Sipacheva (Translator) ISBN 9783030922481, 3030922480, B09S9VJN63

Main subject categories: • Differential geometry • Hypersurfaces • Riemannian manifolds • Lie groupsMathematics Subject Classification: 53-XX • Differential geometryThis 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.