Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] Noel Hicks, Submanifolds of semi-Riemannian manifolds, Rend. Circ. Mat. Palermo (2) 12 (1963), 137–149. MR 0164304,
  • [2] Noel J. Hicks, Notes on differential geometry, Van Nostrand Mathematical Studies, No. 3, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965. MR 0179691
  • [3] Tyuiti Imai, Notes on semi-symmetric metric connections, Tensor (N.S.) 24 (1972), 293–296. Commemoration volumes for Prof. Dr. Akitsugu Kawaguchi’s seventieth birthday, Vol. I. MR 0375121
  • [4] Tyuiti Imai, Hypersurfaces of a Riemannian manifold with semi-symmetric metric connection, Tensor (N.S.) 23 (1972), 300–306. MR 0336597
  • [5] Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol. II, Interscience Tracts in Pure and Applied Mathematics, No. 15 Vol. II, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1969. MR 0238225
  • [6] Kentaro Yano, On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl. 15 (1970), 1579–1586. MR 0275321
  • [7] Kentaro Yano, Integral formulas in Riemannian geometry, Pure and Applied Mathematics, No. 1, Marcel Dekker, Inc., New York, 1970. MR 0284950

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53B25

Retrieve articles in all journals with MSC: 53B25

Additional Information

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

American Mathematical Society