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

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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