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

Erol Kılıç; Mukut Mani Tripathi; Mehmet Gülbahar — 2016

Annales Polonici Mathematici

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 of almost...

Ricci and scalar curvatures of submanifolds of a conformal Sasakian space form

Esmaeil Abedi; Reyhane Bahrami Ziabari; Mukut Mani Tripathi — 2016

Archivum Mathematicum

We introduce a conformal Sasakian manifold and we find the inequality involving Ricci curvature and the squared mean curvature for semi-invariant, almost semi-invariant, $θ$ -slant, invariant and anti-invariant submanifolds tangent to the Reeb vector field and the equality cases are also discussed. Also the inequality involving scalar curvature and the squared mean curvature of some submanifolds of a conformal Sasakian space form are obtained.

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Currently displaying 1 – 8 of 8

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

Ricci and scalar curvatures of submanifolds of a conformal Sasakian space form

Classification of $ξ$ -Ricci-semisymmetric $(κ, μ)$ -manifolds.

On semi-invariant submanifolds of $L P$ -cosymplectic manifolds.

On the concircular curvature tensor of a $(κ, μ)$ -manifold.

On Legendre curves in $α$ -Sasakian manifolds.

A note on Chen's basic equality for submanifolds in a Sasakian space form.

Indefinite almost paracontact metric manifolds.