Differential Geometry

Victor V. Prasolov

ISBN 10: 3030922480 / ISBN 13: 9783030922481

Verlag: Springer Nature Switzerland AG, CH, 2022

Beschreibung

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.

Bestandsnummer des Verkäufers LU-9783030922481

Bibliografische Details

• Titel: Differential Geometry
• Verlag: Springer Nature Switzerland AG, CH
• Erscheinungsjahr: 2022
• Sprache: Englisch
• ISBN-10: 3030922480
• ISBN-13: 9783030922481
• Einband: Hardback
• Auflage: 2022 ed.
• Zustand: New

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

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).