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Almost α-Cosymplectic (κ,μ,ν)-Spaces

Main interest of the present paper is to investigate the almost α-cosymplectic manifolds for which the characteristic vector field of the almost α-cosymplectic structure satisfies a specific (κ,μ,ν)-nullity condition. This condition is invariant under D-homothetic deformation of the almost cosymplectic (κ,μ,ν)-spaces in all dimensions. Also, we prove that for dimensions greater than three, κ,μ,ν are not necessary constant smooth functions such that df^η=0. Then the existence of the three-dimensional case of almost cosymplectic (κ,μ,ν)-spaces are studied. Finally, we construct an appropriate example of such manifolds.