Differential Geometry

Victor V. Prasolov

ISBN 10: 3030922510 / ISBN 13: 9783030922511

Editore: Springer Nature Switzerland AG, CH, 2023

Riguardo questo articolo

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.

Codice articolo LU-9783030922511

Dati bibliografici

• Titolo: Differential Geometry
• Editore: Springer Nature Switzerland AG, CH
• Data di pubblicazione: 2023
• Lingua: Inglese
• ISBN 10: 3030922510
• ISBN 13: 9783030922511
• Rilegatura: Paperback
• Edizione: 2022 ed.
• Condizione: New

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

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).