Geodesic
The Nijenhuis tensor of a pseudo-cosymplectic manifold
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 2, Tome 191 (2021), pp. 149-156.

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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. 
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A. R. Rustanov; S. V. Kharitonova. The Nijenhuis tensor of a pseudo-cosymplectic manifold. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 2, Tome 191 (2021), pp. 149-156. http://geodesic.mathdoc.fr/item/INTO_2021_191_a14/

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