Ricci curvature on warped product submanifolds in spheres with geometric applications

JOURNAL OF GEOMETRY AND PHYSICS

卷:146

Article

Ali, Akram^1,2  Piscoran, Laurian Ioan³  Alkhaldi, Ali H.¹ 

[1] King Khalid Univ, Coll Sci, Dept Math, Abha 9004, Saudi Arabia

[2] Univ Fed Amazonas, Inst Ciencias Exatas, Dept Matemat, Av Gen Rodrigo Octavio, BR-69080900 Manaus, Amazonas, Brazil

[3] Tech Univ Cluj Napoca, North Univ Ctr Baia Mare, Dept Math & Comp Sci Victoriei 76, Baia Mare 430122, Romania

关键词: Ricci curvature;    Warped products;    Riemannian manifolds;    Isometric immersions;    Ordinary differential equation;   

DOI  :  10.1016/j.geomphys.2019.103510

来源: Elsevier

【 摘 要 】

The goal of this paper is to construct a fundamental theorem for the Ricci curvature inequality via partially minimal isometric warped product immersions into an m-dimensional unit sphere S-m, involving the Laplacian of a well defined warping function, the squared norm of a warping function and the squared norm of the mean curvature. Moreover, the equality cases are discussed in detail and some applications are also derived due to involvement of the warping function. As applications, we provide sufficient condition that the base N-1(p) is isometric to the sphere S-P(lambda(1)/p) with constant sectional curvature c = lambda(1)/p The obtained results in the paper give the partial solution of Ricci curvature conjecture, also known as Chen-Ricci inequality obtained by Chen (1999). (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free