Affiliation:
1. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Abstract
In this paper, we use incompressible vector fields for characterizing Killing vector fields. We show that on a compact Riemannian manifold, a nontrivial incompressible vector field has a certain lower bound on the integral of the Ricci curvature in the direction of the incompressible vector field if, and only if, the vector field ξ is Killing. We also show that a nontrivial incompressible vector field ξ on a compact Riemannian manifold is a Jacobi-type vector field if, and only if, ξ is Killing. Finally, we show that a nontrivial incompressible vector field ξ on a connected Riemannian manifold has a certain lower bound on the Ricci curvature in the direction of ξ, and if ξ is also a geodesic vector field, it necessarily implies that ξ is Killing.
Funder
Researchers Supporting Project
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference29 articles.
1. Aris, R. (1989). Vectors, Tensors, and the Basic Equations of FluidMechanics, Dover Publisher.
2. Davidson, P.A. (2017). Introduction to Magnetohydrodynamics, Cambridge University Press. [2nd ed.].
3. Geodesic vector fields and Eikonal equation on a Riemannian manifold;Deshmukh;Indag. Math.,2019
4. Euclidean submanifolds with incompressible canonical vector field;Chen;Sib. Math. J.,2017
5. A link between harmonicity of 2-distance functions and incompressibility of canonical canonical vector fields;Chen;Tamkang J. Math.,2018
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