Hypersurfaces of a Riemannian manifold with a Ricci-quarter symmetric metric connection

Yılmaz, Hülya Bağdatlı (2023) Hypersurfaces of a Riemannian manifold with a Ricci-quarter symmetric metric connection. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 34 (1). pp. 104-111. ISSN 1786-0091

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Abstract

In this paper we study hypersurfaces of a Riemannian manifold endowed with a Ricci-quarter symmetric metric connection. We prove that the induced connection is also a Ricci-quarter symmetric metric connection. We consider the total geodesicness, the total umbilicity and the minimality of a hypersurface of a Riemannian manifold endowed with the Ricci-quarter symmetric metric connection. We obtain the Gauss, Weingarten and Codazzi equations with respect to the Ricci-quarter symmetric metric connection. The relation between the sectional curvatures of M n and M(n+1) with respect to the Ricci-quarter symmetric metric connection has been also given.

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