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

Amira Ishan, Sharief Deshmukh and Gabriel-Eduard Vîlcu
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Amira Ishan: Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Sharief Deshmukh: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Gabriel-Eduard Vîlcu: Department of Cybernetics, Economic Informatics, Finance and Accountancy, Petroleum-Gas University of Ploieşti, Bd. Bucureşti 39, 100680 Ploieşti, Romania

Mathematics, 2021, vol. 9, issue 8, 1-9

Abstract: 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 S m ( c ) 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.

Keywords: Riemannian manifold; sphere; conformal vector field; de-Rham Laplace operator; Fischer–Marsden differential equation; Obata’s differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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