DIFFERENTIAL GEOMETRY AND RIEMANNIAN MANIFOLDS

Name: DIFFERENTIAL GEOMETRY AND RIEMANNIAN MANIFOLDS
Brand: World Scientific
Availability: OutOfStock
Rating: 5 (1 reviews)

By Sauvigny Friedrich

0 - Default Title

Description

This textbook focuses on the study of curves and surfaces, applying modern differential equation theory to geometric problems. By introducing isothermal parameters, it simplifies the fundamental equations of surface theory, leading to clear derivations of results like those of H Hopf and S Bernstein for surfaces of constant and vanishing mean curvature.
Deviating from traditional approaches, the book first treats n-dimensional Riemannian spaces by a corresponding metric, then constructs Riemannian manifolds through transition conditions. The ultimate goal is to prove the Hadamard-Cartan theorem on the diffeomorphic character of the exponential mapping in Riemannian manifolds with nonpositive sectional curvature. By considering curves and surfaces in their optimal parametrization, the resulting ODEs and complex PDEs can be analytically solved, eliminating the need for intricate tensor calculus.
The approach follows that of G Monge in his treatise L'Application de l'Analyse à la Géométrie, applying analytical techniques to geometric problems. Building on this foundation, the book uses modern theory of ODEs and PDEs to study the local and global results for curves and surfaces and their relevant curvatures.

Product details

Number of Pages:

376

Release Date:

2025-10-29

Publication Date:

2025-10-06

Publisher:

World Scientific

Languages:

Original: English

ISBN10:

9819816165

ISBN13:

9789819816163

Weight:

694 g

Height:

157 cm

Width:

235 cm

Thickness:

25 cm

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