Submanifolds of a Riemannian manifold with semisymmetric metric connections

Nakao, Zensho

doi:10.1090/S0002-9939-1976-0445416-9

Submanifolds of a Riemannian manifold with semisymmetric metric connections
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Proc. Amer. Math. Soc. 54 (1976), 261-266 Request permission

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

Noel Hicks, Submanifolds of semi-Riemannian manifolds, Rend. Circ. Mat. Palermo (2) 12 (1963), 137–149. MR 164304, DOI 10.1007/BF02843960
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
Tyuiti Imai, Notes on semi-symmetric metric connections, Tensor (N.S.) 24 (1972), 293–296. MR 375121
Tyuiti Imai, Hypersurfaces of a Riemannian manifold with semi-symmetric metric connection, Tensor (N.S.) 23 (1972), 300–306. MR 336597
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
Kentaro Yano, On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl. 15 (1970), 1579–1586. MR 275321
Kentaro Yano, Integral formulas in Riemannian geometry, Pure and Applied Mathematics, No. 1, Marcel Dekker, Inc., New York, 1970. MR 0284950