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Some Conditions on Trans-Sasakian Manifolds to Be Homothetic to Sasakian Manifolds

Author

Listed:
  • Sharief Deshmukh

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

  • Amira Ishan

    (Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Olga Belova

    (Institute of Physical and Mathematical Sciences and IT, Immanuel Kant Baltic Federal University, A. Nevsky Str. 14, 236016 Kaliningrad, Russia)

  • Suha B. Al-Shaikh

    (Information Technology Department, Arab Open University, P.O. Box 84901, Hittin 11681, Saudi Arabia)

Abstract

In this paper, we study 3-dimensional compact and connected trans-Sasakian manifolds and find necessary and sufficient conditions under which these manifolds are homothetic to Sasakian manifolds. First, four results in this paper deal with finding necessary and sufficient conditions on a compact and connected trans-Sasakian manifold to be homothetic to a compact and connected Sasakian manifold, and the fifth result deals with finding necessary and sufficient condition on a connected trans-Sasakian manifold to be homothetic to a connected Sasakian manifold. Finally, we find necessary and sufficient conditions on a compact and simply connected trans-Sasakian manifold to be homothetic to a compact and simply connected Einstein Sasakian manifold.

Suggested Citation

  • Sharief Deshmukh & Amira Ishan & Olga Belova & Suha B. Al-Shaikh, 2021. "Some Conditions on Trans-Sasakian Manifolds to Be Homothetic to Sasakian Manifolds," Mathematics, MDPI, vol. 9(16), pages 1-10, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1887-:d:610625
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