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A Note on Geodesic Vector Fields

Author

Listed:
  • Sharief Deshmukh

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

  • Josef Mikeš

    (Department of Algebra and Geometry, Palacky University, 17. Listopadu 12, 77146 Olomouc, Czech Republic)

  • Nasser Bin Turki

    (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, Ploieşti 100680, Romania)

Abstract

The concircularity property of vector fields implies the geodesicity property, while the converse of this statement is not true. The main objective of this note is to find conditions under which the concircularity and geodesicity properties of vector fields are equivalent. Moreover, it is shown that the geodesicity property of vector fields is also useful in characterizing not only spheres, but also Euclidean spaces.

Suggested Citation

  • Sharief Deshmukh & Josef Mikeš & Nasser Bin Turki & Gabriel-Eduard Vîlcu, 2020. "A Note on Geodesic Vector Fields," Mathematics, MDPI, vol. 8(10), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1663-:d:420259
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