Optimal Inequalities for Submanifolds of an Indefinite Space Form

Optimal inequalities involving the scalar curvature, the mean curvature vector and the second fundamental form for pseudo Riemannian submanifolds are proved and the equality cases of these inequalities are discussed. These results are studied for submanifolds of various indefinite contact space forms

A USEFUL ORTHONORMAL BASIS ON BI-SLANT SUBMANIFOLDS OF ALMOST HERMITIAN MANIFOLDS

In this paper, we study bi-slant submanifolds of an almost Hermitian manifold for different cases. We introduce a new orthonormal basis on bi-slant submanifold, semi-slant submanifold and hemi-slant submanifold of an almost Hermitian manifold to compute Chen’s main inequalities. We investigate these inequalities for semi-slant submanifolds, hemi-slant submanifolds and slant submanifolds of a generalized complex space form. We obtain some characterizations on such submanifolds of a complex space form

Some Characterizations of Semi-Invariant Submanifolds of Golden Riemannian Manifolds

In this paper, we study some characterizations for any submanifold of a golden Riemannian manifold to be semi-invariant in terms of canonical structures on the submanifold, induced by the golden structure of the ambient manifold. Besides, we determine forms of the distributions involved in the characterizations of a semi-invariant submanifold on both its tangent and normal bundles

Warped product submanifolds of Lorentzian paracosymplectic manifolds

In this paper we study the warped product submanifolds of a Lorentzian paracosymplectic manifold and obtain some nonexistence results. We show that a warped product semi-invariant submanifold in the form {$M=M_{T}\times_{f}M_{\bot}$} of Lorentzian paracosymplectic manifold such that the characteristic vector field is normal to $M$ is an usual Riemannian product manifold where totally geodesic and totally umbilical submanifolds of warped product are invariant and anti-invariant, respectively. We prove that the distributions involved in the definition of a warped product semi-invariant submanifold are always integrable. A necessary and sufficient condition for a semi-invariant submanifold of a Lorentzian paracosymplectic manifold to be warped product semi-invariant submanifold is obtained. We also investigate the existence and nonexistence of warped product semi-slant and warped product anti-slant submanifolds in a Lorentzian paracosymplectic manifold.Comment: This paper has been withdrawn by the autho

Inequalities for scalar curvature of pseudo-Riemannian submanifolds

Some basic inequalities, involving the scalar curvature and the mean curvature, for a pseudo-Riemannian submanifold of a pseudo-Riemannian manifold are obtained. We also find inequalities for spacelike submanifolds. Equality cases are also discussed