Conformal Vector Fields and the De-Rham Laplacian on a Riemannian Manifold

Mathematics

Gabriel-Eduard Vîlcu¹  Sharief Deshmukh²  Amira Ishan³ 

[1] Department of Cybernetics, Economic Informatics, Finance and Accountancy, Petroleum-Gas University of Ploieşti, Bd. Bucureşti 39, 100680 Ploieşti, Romania;Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia;Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia;

关键词: Riemannian manifold;    sphere;    conformal vector field;    de-Rham Laplace operator;    Fischer–Marsden differential equation;    Obata’s differential equation;   

DOI  :  10.3390/math9080863

来源: DOAJ

【 摘 要 】

We study the effect of a nontrivial conformal vector field on the geometry of compact Riemannian spaces. We find two new characterizations of the m-dimensional sphere ${\mathbf{S}}^m\left(c\right)$ of constant curvature c. The first characterization uses the well known de-Rham Laplace operator, while the second uses a nontrivial solution of the famous Fischer–Marsden differential equation.

【 授权许可】

Unknown