Geodesic
Generalized Kenmotsu manifold constancy of type
Čebyševskij sbornik, Tome 20 (2019) no. 2, pp. 7-21

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In this work we consider generalized Kenmotsu manifolds, we introduce: the fourth and the fifth fundamental identities of generalized Kenmotsu manifolds; the first and the second structural tensors of generalized Kenmotsu manifolds (and we prove their properties); the concept of adjoint Q-algebra for generalized Kenmotsu manifolds. We prove that generalized Kenmotsu manifolds and the II kind special generalized Kenmotsu manifolds have anticommutative adjoint Q-algebra. And the Kenmotsu manifolds and the I kind special generalized Kenmotsu manifolds have Abelian adjoint Q-algebra. The type constancy contact analog is introduced and the constant-type generalized Kenmotsu manifolds are thoroughly examined. We have identified the type point constancy conditions of the generalized Kenmotsu manifolds in the adjoint G-structure space. We prove that the zero constant type GK-manifold class coincides with the Kenmotsu manifold class and the non-zero constant type GK-manifold class can be concircularly transformed into the almost contact metric manifolds locally equivalent to the product of the six dimensional NK-eigenmanifold and the real straight line.
Keywords: Kenmotsu manifolds, generalized Kenmotsu manifolds, the I kind special generalized Kenmotsu manifolds, the II kind special generalized Kenmotsu manifolds, constant type GK-manifolds, most precise cosymplectic manifold. 
@article{CHEB_2019_20_2_a0,
     author = {Ahmad Abu-Saleem and A. R. Rustanov and T. L. Melekhina},
     title = {Generalized {Kenmotsu} manifold constancy of type},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {7--21},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2019_20_2_a0/}
}
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Ahmad Abu-Saleem; A. R. Rustanov; T. L. Melekhina. Generalized Kenmotsu manifold constancy of type. Čebyševskij sbornik, Tome 20 (2019) no. 2, pp. 7-21. http://geodesic.mathdoc.fr/item/CHEB_2019_20_2_a0/