Заседание научного семинара кафедры 18 декабря 2019г.
23.12.2019
Abstract. In this work we consider generalized Kenmotsu manifolds, we introduce:
1) the fourth and the fifth fundamental identities of generalized Kenmotsu manifolds;
2) the first and the second structural tensors of generalized Kenmotsu manifolds (and we prove their properties);
3) the concept of adjoint Q-algebra for generalized Kenmotsu manifolds.
We prove that generalized Kenmotsu manifolds and the 2nd kind special generalized Kenmotsu manifolds have anticommutative adjoint Q-algebra.
And the Kenmotsu manifolds and the 1st 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.
1) the fourth and the fifth fundamental identities of generalized Kenmotsu manifolds;
2) the first and the second structural tensors of generalized Kenmotsu manifolds (and we prove their properties);
3) the concept of adjoint Q-algebra for generalized Kenmotsu manifolds.
We prove that generalized Kenmotsu manifolds and the 2nd kind special generalized Kenmotsu manifolds have anticommutative adjoint Q-algebra.
And the Kenmotsu manifolds and the 1st 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.