Submanifolds of a Riemannian Manifold with Semisymmetric Metric Connections

We derive the Gauss curvature equation and the Codazzi-Mainardi equation with respect to a semisymmetric metric connection on a Riemannian manifold and the induced one on a submanifold. We then generalize the theorema egregium of Gauss.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1976-01, Vol.54 (1), p.261-266
Main Author: Nakao, Zensho
Format: Article
Language:English
Subjects:
Curvature
Gauss equations
Hypersurfaces
Riemann manifold
Tangents
Tensors
Vector fields
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Description
Summary:We derive the Gauss curvature equation and the Codazzi-Mainardi equation with respect to a semisymmetric metric connection on a Riemannian manifold and the induced one on a submanifold. We then generalize the theorema egregium of Gauss.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-1976-0445416-9