arXiv subjects
Publications and source records attributed to Aysel Turgut Vanli.
In this paper, we study on semi-invariant submanifolds of normal complex contact metric manifolds. We give the definition of such submanifolds and we obtain useful relations. Moreover, we give the integrability conditions of distributions.
In this paper, we present the invalidities of the results in [3], because of their definition of a semi-invariant submanifold of an almost complex contact metric manifold is not true .
In this article we study a class of normalθcomplexθcontactθmetricθmanifold which is called a complex Sasakian manifold. This kind of manifold has a globally defined complex contact form and normal complex contact structure. We give the definition of a complex Sasakian manifold by consider the real case and we present general properties. Also we obtain some useful curvature relations. Finally we examine flatness conditions for general curvature tensor B.
In this paper, we study normal complex contact metric manifolds and we get some general results on them. Moreover, we obtained the general expression of the curvature tensor field for arbitrary vector fields. Furthermore, we show that the necessary and succient conditions to be normal a complex contact metric manifold. Also, we give some new equailities for Ricci curvature of normal complex contact metric manifolds.
In this paper, invariant submanifolds of a generalized Kenmotsu manifold are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be an invariant submanifold.In this case, we investigate further properties of invariant submanifolds of \ a generalized Kenmotsu manifold. In addition, some theorems are given related to an invariant submanifold of a generalized Kenmotsu manifold.We consider semiparallel and 2-semiparallel invariant submanifolds of a generalized Kenmotsu manifold.
In 1972, K. Kenmotsu studied a class of almost contact Riemannian manifolds. Later, such a manifold was called a Kenmotsu manifold. This paper, we studied Kenmotsu manifolds with $(2n+s)$-dimensional $s-$contact metric manifold and this manifold, we have called generalized Kenmotsu manifolds. Necessary and sufficient condition is given for an almost $s-$contact metric manifold to be a generalized Kenmotsu manifold.We show that a generalized Kenmotsu manifold is a locally warped product space. In addition, we study some curvature properties of generalized Kenmotsu manifolds. Moreover, we show that the $φ$% -sectional curvature of any semi-symmetric and projective semi-symmetric $% (2n+s)$-dimensional generalized Kenmotsu manifold is $-s$.