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

Sharief Deshmukh, Amira Ishan, Olga Belova and Suha B. Al-Shaikh
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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

Mathematics, 2021, vol. 9, issue 16, 1-10

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.

Keywords: trans-Sasakian manifolds; Sasakian manifolds; Einstein Sasakian manifolds; scalar curvature (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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