Bi-warped products and applications in locally product Riemannian manifolds

JOURNAL OF GEOMETRY AND PHYSICS

卷:144

Article

Al-Jedani, Awatif¹  Uddin, Siraj¹  Alghanemi, Azeb¹  Mihai, Ion² 

[1] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah 21589, Saudi Arabia

[2] Univ Bucharest, Fac Math, Str Acad, Bucharest 14010014, Romania

关键词: Warped products;    Bi-warped products;    Multiply warped products;    Slant submanifolds;    Pointwise slant submanifolds;    Dirichlet energy;    Locally product Riemannian manifold;   

DOI  :  10.1016/j.geomphys.2019.06.001

来源: Elsevier

【 摘 要 】

In this paper, we consider M-theta, a pointwise slant submanifold and prove that every bi-warped product M-perpendicular to x(f1), M-T x(f2) M-theta in a locally product Riemannian manifold satisfies a general inequality: parallel to sigma parallel to(2) >= n(2)parallel to(del) over right arrow (T)(lnf(1))parallel to(2) + n(3) cos(2) theta parallel to(del) over right arrow (theta)(lnf(2))parallel to(2), where n(2) = dim(M-T), n(3) = dim(M-theta) and sigma is the second fundamental form and del(T)(lnf(1)) and del(theta)(Inf(2)) are the gradient components along M-T and M-theta, respectively. We also discuss the equality case of this inequality. Furthermore, we give some applications and non-trivial examples. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free