Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On f-cosymplectic and (k, µ)-cosymplectic Manifolds Admitting Fischer -Marsden Conjecture

  • Received : 2022.08.10
  • Accepted : 2022.11.28
  • Published : 2023.09.30
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Abstract

The aim of this paper is to study the Fisher-Marsden conjucture in the frame work of f-cosymplectic and (k, µ)-cosymplectic manifolds. First we prove that a compact f-cosymplectic manifold satisfying the Fisher-Marsden equation R'*g = 0 is either Einstein manifold or locally product of Kahler manifold and an interval or unit circle S1. Further we obtain that in almost (k, µ)-cosymplectic manifold with k < 0, the Fisher-Marsden equation has a trivial solution.

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Acknowledgement

This work was supported by University Grants Commission, New Delhi, India(UGC-Ref-No: 942/(CSIR-UGC NET DEC, 2018).

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