On f-cosymplectic and (k, µ)-cosymplectic Manifolds Admitting Fischer-Marsden Conjecture
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The aim of this paper is to study the Fisher-Marsden conjucture on 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 an Einstein manifold or a local product of a Kahler manifold and an interval or a unit circle S1 . Further we obtain that in almost (k, µ)-cosymplectic manifolds with k < 0, the Fisher-Marsden equation has a trivial solution.
Abstract
The aim of this paper is to study the Fisher-Marsden conjucture on 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 an Einstein manifold or a local product of a Kahler manifold and an interval or a unit circle S1 . Further we obtain that in almost (k, µ)-cosymplectic manifolds with k < 0, the Fisher-Marsden equation has a trivial solution.
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