Abstract
The main purpose of this paper is to study almost α -cosymplectic pseudo metric manifold satisfying certain η -parallel tensor fields. We first focus on the concept of almost α -cosymplectic pseudo metric manifold and its curvature properties. Then, we obtain some results related to the η -parallelity of h , φ h , and τ . Moreover, the deformation of almost α -Kenmotsu pseudo metric structure is given. We conclude the paper with an illustrative example of almost α -cosymplectic pseudo metric manifold.
Highlights
Manifolds known as almost contact metric manifolds have been studied in [1,2,3]. e class of almost contact metric manifolds which are called almost Kenmotsu manifolds is firstly introduced by Kenmotsu. ese manifolds appear for the first time in [4], where they have been locally classified
Wang and Liu introduced the geometry of almost Kenmotsu pseudo metric manifolds [12]. ey emphasized the analogies and differences in connection with the Riemann metric tensor and obtained certain classification results related to locally symmetry and nullity condition
A systematic study of almost α-cosymplectic pseudo manifolds has not been undertaken yet. e main purpose of this paper is to contribute to future studies on this subject
Summary
Manifolds known as almost contact metric manifolds have been studied in [1,2,3]. e class of almost contact metric manifolds which are called almost Kenmotsu manifolds is firstly introduced by Kenmotsu. ese manifolds appear for the first time in [4], where they have been locally classified. Manifolds known as almost contact metric manifolds have been studied in [1,2,3]. E class of almost contact metric manifolds which are called almost Kenmotsu manifolds is firstly introduced by Kenmotsu. Kim and Pak have introduced a wide subclass of almost contact metric manifolds called almost α-cosymplectic manifolds [5]. Naik et al studied Kenmotsu pseudo metric manifolds. The authors established necessary and sufficient conditions for Kenmotsu pseudo metric manifolds satisfying certain tensor conditions [13]. In [16], Ghosh et al studied the η-parallelity of the torsion tensor τ for a contact metric manifold M2n+1. Ese formulas would enable us to find the geometrical properties of almost α-cosymplectic pseudo metric manifolds with η-parallel tensor h and φh. We give an illustrative example of almost α-cosymplectic pseudo metric manifolds
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