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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We apply the obtained results to slant submanifolds.
📌 3 Key Takeaways
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Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact:We apply the obtained results to slant submanifolds.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Generalized S-space-form · intrinsic invariant · slant submanifold
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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Cite This Article
Fernández, L., Fuentes, A. (2015). Some relationships between intrinsic and extrinsic invariants of submanifolds in generalized $S$-space-forms. Hacettepe Journal of Mathematics and Statistics, Volume: 44 Issue: 1. https://ajindex.com/articles/1403325