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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Submanifolds of a Riemannian manifold with semisymmetric metric connections


Author: Zensho Nakao
Journal: Proc. Amer. Math. Soc. 54 (1976), 261-266
MSC: Primary 53B25
MathSciNet review: 0445416
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Abstract: 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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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0445416-9
PII: S 0002-9939(1976)0445416-9
Keywords: Codazzi-Mainardi equation, conformally flat space, Gauss curvature equation, mean curvature normal, sectional curvature, semisymmetric metric connection, totally umbilical submanifold
Article copyright: © Copyright 1976 American Mathematical Society