Generalized Kenmotsu manifold constancy of type
Ahmad Abu-Saleema, A. R. Rustanovb, T. L. Melekhinac
a Al al-Bayt University (Mafraq,
b Federal state budget educational institution
of higher education "NATIONAL RESEARCH MOSCOW STATE UNIVERSITY OF CIVIL
ENGINEERING" (NRU MGSU) (Moscow)
c Financial University under the
Government of the Russian Federation (Moscow)
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.
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.
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Ahmad Abu-Saleem, A. R. Rustanov, T. L. Melekhina, “Generalized Kenmotsu manifold constancy of type”, Chebyshevskii Sb., 20:2 (2019), 7–21
Citation in format AMSBIB
\by Ahmad~Abu-Saleem, A.~R.~Rustanov, T.~L.~Melekhina
\paper Generalized Kenmotsu manifold constancy of type
\jour Chebyshevskii Sb.
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