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Geodesic Vector Fields on a Riemannian Manifold

Author

Listed:
  • Sharief Deshmukh

    (Department of Mathematics, College of science, King Saud University, P.O. Box-2455 Riyadh 11451, Saudi Arabia)

  • Patrik Peska

    (Department of Algebra and Geometry, Palacky University, 77146 Olomouc, Czech Republic)

  • Nasser Bin Turki

    (Department of Mathematics, College of science, King Saud University, P.O. Box-2455 Riyadh 11451, Saudi Arabia)

Abstract

A unit geodesic vector field on a Riemannian manifold is a vector field whose integral curves are geodesics, or in other worlds have zero acceleration. A geodesic vector field on a Riemannian manifold is a smooth vector field with acceleration of each of its integral curves is proportional to velocity. In this paper, we show that the presence of a geodesic vector field on a Riemannian manifold influences its geometry. We find characterizations of n -spheres as well as Euclidean spaces using geodesic vector fields.

Suggested Citation

  • Sharief Deshmukh & Patrik Peska & Nasser Bin Turki, 2020. "Geodesic Vector Fields on a Riemannian Manifold," Mathematics, MDPI, vol. 8(1), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:137-:d:310483
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