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Displaying similar documents to “Ricci and Casorati principal directions of δ ( 2 ) Chen ideal submanifolds”

On an inequality of Oprea for Lagrangian submanifolds

Franki Dillen, Johan Fastenakels (2009)

Open Mathematics

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We show that a Lagrangian submanifold of a complex space form attaining equality in the inequality obtained by Oprea in [8], must be totally geodesic.

Chen-Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds

Erol Kılıç, Mukut Mani Tripathi, Mehmet Gülbahar (2016)

Annales Polonici Mathematici

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Some examples of slant submanifolds of almost product Riemannian manifolds are presented. The existence of a useful orthonormal basis in proper slant submanifolds of a Riemannian product manifold is proved. The sectional curvature, the Ricci curvature and the scalar curvature of submanifolds of locally product manifolds of almost constant curvature are obtained. Chen-Ricci inequalities involving the Ricci tensor and the squared mean curvature for submanifolds of locally product manifolds...

Totally umbilical submanifolds in some semi-Riemannian manifolds

Stanisław Ewert-Krzemieniewski (2010)

Colloquium Mathematicae

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We investigate totally umbilical submanifolds in manifolds satisfying some curvature conditions of either recurrent or pseudosymmetry type in the sense of Ryszard Deszcz and derive the respective condition for submanifolds. We also prove some relations involving the mean curvature and the Weyl conformal curvature tensor of submanifolds. Some examples are discussed.