2012
DOI: 10.4134/ckms.2012.27.4.781
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Semi-Riemannian Submanifolds of a Semi-Riemannian Manifold With a Semi-Symmetric Non-Metric Connection

Abstract: Abstract. We study some properties of a semi-Riemannian submanifold of a semi-Riemannian manifold with a semi-symmetric non-metric connection. Then, we prove that the Ricci tensor of a semi-Riemannian submanifold of a semi-Riemannian space form admitting a semi-symmetric non-metric connection is symmetric but is not parallel. Last, we give the conditions under which a totally umbilical semi-Riemannian submanifold with a semi-symmetric non-metric connection is projectively flat.

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