2015•Hacettepe Journal of Mathematics and StatisticsOpen access

Some relationships between intrinsic and extrinsic invariants of submanifolds in generalized S-space-forms

Luis M. Fernández

Abstract

We establish some inequalities of Chen's type between certain intrinsic invariants (involving sectional, Ricci and scalar curvatures) and the squared mean curvature of submanifolds tangent to the structure vector fields of a generalized S-space-form and we discuss the equality cases of them. We apply the obtained results to slant submanifolds.

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Key concepts: Space form, Mathematics, Tangent, Pure mathematics, Scalar curvature, Second fundamental form, Space (punctuation), Scalar (mathematics)