The Nijenhuis tensor of a pseudo-cosymplectic manifold

A. R. Rustanov^a, S. V. Kharitonova<sup>b

a</sup> Moscow State University of Civil Engineering
^b Orenburg State University

Abstract: In this paper, we examine the Nijenhuis tensor of pseudo-cosymplectic manifolds. The adjoint $G$-structure of an almost contact metric manifold is constructed, the first group of such manifolds is defined. The pseudo-cosymplectic subclass of quasi-cosymplectic manifolds is distinguished and the first group of structure equations is obtained for them. We obtained necessary and sufficient conditions under which a pseudo-cosymplectic manifold is cosymplectic, most precisely cosymplectic, normal, or integrable.

Keywords: almost contact metric structure, Nijenhuis tensor, quasi-cosymplectic structure, pseudo-cosymplectic structure, most precisely cosymplectic structure.

UDC: 514.76

MSC: 53D15, 53C25

DOI: 10.36535/0233-6723-2021-191-149-156

 English version: Journal of Mathematical Sciences (New York), 2025, 288:6, 814–821