Almost {\alpha}-Cosymplectic ({\kappa},{\mu},{\nu})-Spaces

TL;DR

This paper investigates almost lpha-cosymplectic manifolds satisfying a specific nullity condition, analyzing their invariance under deformation, the constancy of parameters in higher dimensions, and providing a concrete example.

Contribution

It introduces the concept of almost lpha-cosymplectic ({ppa},{\u00Mu},{nu})-spaces, studies their properties under deformation, and explores the existence of such structures in three dimensions with an explicit example.

Findings

The ({ppa},{nu},{nu})-nullity condition is invariant under D-homothetic deformation.

In dimensions greater than three, ppa, nu, nu are not necessarily constant functions.

Existence of three-dimensional almost lpha-cosymplectic ({ppa},{nu},{nu})-spaces is established.

Abstract

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