Bi-warped products and applications in locally product Riemannian manifolds
| Autor: | Azeb Alghanemi, Awatif AL-Jedani, Siraj Uddin, Ion Mihai |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pointwise
Pure mathematics Second fundamental form 010102 general mathematics General Physics and Astronomy Riemannian manifold Submanifold 01 natural sciences Product (mathematics) 0103 physical sciences 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematical Physics Mathematics |
| Zdroj: | Journal of Geometry and Physics. 144:358-369 |
| ISSN: | 0393-0440 |
| DOI: | 10.1016/j.geomphys.2019.06.001 |
| Popis: | In this paper, we consider M θ , a pointwise slant submanifold and prove that every bi-warped product M ⊥ × f 1 M T × f 2 M θ in a locally product Riemannian manifold satisfies a general inequality: ‖ σ ‖ 2 ≥ n 2 ‖ ∇ → T ( ln f 1 ) ‖ 2 + n 3 cos 2 θ ‖ ∇ → θ ( ln f 2 ) ‖ 2 , where n 2 = dim ( M T ) , n 3 = dim ( M θ ) and σ is the second fundamental form and ∇ T ( ln f 1 ) and ∇ θ ( ln f 2 ) are the gradient components along M T and M θ , respectively. We also discuss the equality case of this inequality. Furthermore, we give some applications and non-trivial examples. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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