Isotropic submanifolds of pseudo-Riemannian spaces

Abstract

The family of all the submanifolds of a given Riemannian or pseudo-Riemannian manifold is large enough to classify them into some interesting subfamilies such as minimal (maximal), totally geodesic, Einstein, etc. Most of these have been extensively studied by many authors, but as far as we know, no paper has hitherto been published on the class of isotropic submanifolds. The purpose of this paper is therefore to gain a better understanding of this interesting class of submanifolds that arise naturally in mathematics and physics by studying their relationships with other closely distinguised families.Mathematics Subject Classification: 53C25, 53C40

Inequalities on Isotropic Submanifolds in Pseudo-Riemannian Space Forms

“…Obviously, this is a generalization of the totally umbilical immersion. For isotropic submanifolds in the pseudo-Riemannian settings we cite [1].…”

“…for X, Y, Z ∈ X (M n s ), which is an equivalent condition for the submanifold M n s to be isotropic (see [1], Theorem 3.…”

“…Inequalities on Isotropic Submanifolds in Pseudo-Riemannian Space Forms where h q ij are the coefficients of the second fundamental form. On the other hand, the formula (6) from [1] gives the relation…”

“…To find examples of isotropic Lorentzian submanifolds in pseudo-Riemannian space forms of signature 1 satisfying the equality case in Theorem 4. 1…”

Chen Inequalities for Isotropic Submanifolds in Pseudo-Riemannian Space Forms

“…The concept of an isotropic submanifold of a Riemannian manifold was extended to submanifolds in pseudo-Riemannian manifolds by Cabrerizo et al [1].…”