Almost α-Paracosymplectic Manifolds

Abstract

This paper is a complete study of almost α-paracosmplectic manifolds. We characterize almost α-paracosmplectic manifolds which have para Kaehler leaves. Main curvature identities which are fulfilled by any almost α-paracosmplectic manifold are found. We also proved that ξ is a harmonic vector field if and only if it is an eigen vector field of the Ricci operator. We locally classify three dimensional almost α-para-Kenmotsu manifolds satisfying a certain nullity condition. We show that this condition is invariant under D_{γ,β}-homothetic deformation. Furthermore, we construct examples of almost α-paracosmplectic manifolds satisfying generalized nullity conditions

30 pages

References in corpus (3)

• A survey on cosymplectic geometry
• On basic curvature identities for almost (para)contact metric manifolds
• Five dimensional almost para-cosymplectic manifolds with contact Ricci potential

Cited by in corpus (5)

• Geometry of $\mathcal{PR}$-semi-invariant warped product submanifolds in paracosymplectic manifold
• Yamabe Solitons on three-dimensional normal almost paracontact metric manifolds
• Rank of Jacobi operator and existence of quadratic parallel differential form, with applications to geometry of almost para-contact metric manifolds
• Pointwise Semi-Slant Warped Product Submanifold in a Lorentzian Paracosymplectic Manifold
• $\mathcal{PR}$-anti-slant warped product submanifold of a nearly paracosymplectic manifold