Differential Geometry
Springer International Publishing (Verlag)
978-3-030-92248-1 (ISBN)
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.
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).
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.
"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)
“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)
| Erscheinungsdatum | 12.02.2022 |
|---|---|
| Reihe/Serie | Moscow Lectures |
| Übersetzer | Olga Sipacheva |
| Zusatzinfo | XI, 271 p. 1 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 583 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | Differential Geometry • first fundamental form • Gaussian curvature • geometry of surfaces • Second fundamental form • theorem of Gauss Bonnet |
| ISBN-10 | 3-030-92248-0 / 3030922480 |
| ISBN-13 | 978-3-030-92248-1 / 9783030922481 |
| Zustand | Neuware |
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