Abstract
In this paper, we concentrated our attention on geometry of generalized projective tensor of nearly cosymplectic manifold. In particular, we studied the flatness property of generalized projective tensor. This property helped us to find the necessary and sufficient condition that nearly cosymplectic manifold is a generalized Einstein manifold.
Highlights
One of the important curvature tensors is the projective tensor
We concentrated our attention on geometry of generalized projective tensor of nearly cosymplectic manifold
Abood [3] studied the projective tensor of nearly Kahler manifold
Summary
One of the important curvature tensors is the projective tensor. According to this importance, many authors focused on its geometrical properties. Received by the editors: June 20, 2018; Accepted: September 30, 2019. Cosymplectic manifold, generalized projective curvature tensor, generalized Einstein manifold. Let M be a smooth manifold of dimension 2n + 1 greater than 3, X(M ) be the module of smooth vector ...elds on M , Xc(M ) be the complexi...cation of the module X(M ) and Tpc(M ) be the complexi...cation of tangent space Tp(M ) at the point p 2 M. An almost contact manifold (AC-manifold) is the set (M; ; ; ; g), where is di¤erential 1-form called a contact form, is a vector ...eld called a characteristic, is endomorphism of X(M ) called a structure endomorphisim and g = h:; :i is the Riemannian metric on M.
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