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On Gaussian and Geodesic Curvature of Riemannian Manifolds

Name: On Gaussian and Geodesic Curvature of Riemannian Manifolds
Creator: Hansklaus Rummler
Keywords: Local Riemannian geometry, Characteristic classes and numbers in differential topology, Integral geometry, 0101 mathematics, 01 natural sciences

On Gaussian and geodesic curvature of Riemannian manifolds

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 1974Publisher:Canadian Mathematical SocietyJournal:Canadian Journal of Mathematics, volume 26, pages 629-635 (issn: 0008-414X, eissn: 1496-4279,

Authors: Hansklaus Rummler;

doi: 10.4153/cjm-1974-060-x

On Gaussian and Geodesic Curvature of Riemannian Manifolds

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Abstract

In [1], S. S. Chern gave a very elegant and simple proof of the Gauss-Bonnet formula for closed (i.e. compact without boundary) oriented Riemannian manifolds of even dimension:Here, c is a suitable constant depending on the dimension of M and Ω is an n-form (n = dim M) which may be calculated from its curvature tensor. W. Greub gave a coordinate-free description of this integrand Ω (cf. [4]).

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University of Toronto
Canada

Keywords

Local Riemannian geometry, Characteristic classes and numbers in differential topology, Integral geometry

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