CONTACT CONFORMAL IN -SASAKIAN MANIFOLD

gazi university journal of science, 2019

Journal of Mountain Research

We study of complex sasakian manifold which is a type of normal complex contact metric manifold and study of complex -Einstein sasakian manifold [Vanli and Unal, 2017]. Inan Unal and A. Turgut Vanli obtained curvature properties of complex Sasakian manifold [Vanli and Unal, 2019]. We define some relations between curvature tensors of complex Sasakian manifold and obtained some useful results.

Georgian Mathematical Journal

We study the conformal curvature tensor and the contact conformal curvature tensor in Sasakian and/or K-contact manifolds. We find a necessary and sufficient condition for a Sasakian manifold to be ϕ-conformally flat. We also find some necessary conditions for a K-contact manifold to be ϕ-contact conformally flat. Then we give a structure theorem for ϕ-contact conformally flat Sasakian manifolds. It is also proved that a Sasakian manifold cannot be ξ-contact conformally flat.

The purpose of the paper is to study the notion of CR-submanifold and the existence of some structures on a hypersurface of a quarter symmetric non metric connection in a quasi-Sasakian man-ifold. We study the existence of a Kahler structure on M and the existence of a globally metric frame f-structure in sence of Goldberg S.I., Yano K. [6]. We discuss the integrability of distributions on M and geometry of their leaves. We have tries to relate this result with those before obtained by Goldberg V., Rosca R. devoted to Sasakian manifold and conformal connections. Key words and phrases: CR-submanifold, quasi-Sasakian manifold, quarter symmetric non metric connection, integrability conditions of the distributions.

We obtain results on the vanishing of divergence of Concircular curvature tensor with respect to semi-symmetric metric connection on K-contact and trans-Sasakian manifolds.

The object of the present paper is to initiate the study contact CR-submanifolds of a nearly trans-hyperbolic Sasakian manifold with a quarter symmetric semi metric connection. For this, some properties of CR-submanifolds of a nearly trans-hyperbolic Sasakian manifold with a quarter symmetric semi metric connection are investigated which conclude that CR-submanifolds of a nearly trans-hyperbolic Sasakian manifold with a quarter symmetric semi metric connection exists with respect to the í µí¼‰−horizontal and í µí¼‰−vertical.

2016

Abstract. In the present paper, biharmonic almost contact curves with respect to generalized Tanaka Webster Okumura connections have been studied on three-dimensional trans-Sasakian manifolds. Locally phi-symmetric almost contact curves on three-dimensional trans-Sasakian manifolds with respect to generalized Tanaka Webster Okumura connections have been introduced. Hyperbolic space as a particular case of trans-Sasakian manifolds has been studied. Examples of almost contact curves are given.

Lobachevskii Journal of Mathematics, 2014

The object of the present paper is to study quasi-conformally flat trans-Sasakian manifolds. We consider trans-Sasakian manifolds with η-parallel and cyclic parallel Ricci tensors. φ-Ricci symmetric quasi-conformally flat trans-Sasakian manifolds have been studied. We also investigates quasi-conformally flat trans-Sasakian manifolds which are Einstein Semi-symmetric.

Periodica Mathematica Hungarica, 1996

Let M be a S-dimensional quasi-Sasakian manifold. On such a manifold, the so-called structure function /3 is defined. With the help of this fuuction, we find necessary and sufficient conditions for hf to be conformally flat. Next it is proved that if M is additionally conformally flat with p = const., then (a) A/r is locally a product of R and a P-dimensional Ktilerian space of constant Gauss curvature (the cosymplectic case), or (b) M is of constant positive curvature (the non cosymplectic case; here the quasi-Sasakian structure is homothetic to a Sasakian structure). An example of a J-dimensional quasi-Sasakian structure being conformally flat with nonconstant structure function is also described. For conformally flat quasi-Sasakian manifolds of higher dimensions see [Ol] 1. Introduction An almost contact metric manifold M and its almost contact metric structure (4, I, 7, g) are said to be quasi-Sasakian if the structure is normal and the funclamental a-form @ is closed. The notion of quasi-Sasakian structures was introduced and the first examples were given by Blair [BI]. The simplest examples of quasi-Sasakian structures are those being cosymplectic (i.e., normal with dq = 0. and d@ = 0; here rank 71 = 1) as well as Sa.sa.kian (i.e., normal with dq = +, here za.m& T) = 2n + 1 = dim hf). Homogeneous quasi-Sasakian structnres on the m EMsenberg groups were constructed by Gonzalez and C!binea [GC]. Products of (quasi-)Sasakian manifolds and KLhlerian manifolds a.re also quasirsasakian. Certain sufficient conditions for a quasi-Sasakian manifold to be locally such a product are studied by Blair [Bl], Tanno [T] and Kaaemaki (Kal, Kaz]. It is also known that D-homathetic and homothetic deformatiions of (quasi-)Sasakian structures lead to quasi-Sasakian structures (cf. the author r&J).

2017

The purpose of the present paper is to study contact CR-submanifolds of aδLorentzian trans-Sasakian manifold with a quarter symmetric non-metric c onnection. Also, we investigate the relation between the curvature tensor of δ-Lorentzian trans-Sasakian manifolds and related results with respect to the quarter symmetric non-metric conne ction and the LeviCivita connection. 1. I NTRODUCTION The notion ofCR-submanifolds of a Kaehler manifold was introduced by A. Bejancu [1]. Later on,CR-submanifolds of a Sasakian manifold were studied by M. Kobayashi [11] . K. Matsumoto introduced the idea of a Lorentzian para-Sasakian structure and s tudied several of its properties [6]. J. A. Oubina defined and studied a new class of almost co ntact metric manifold known as trans-Sasakian manifold, which includes α-Sasakian,β-Kenmotsu and cosymplectic structures [5]. M. H. Shahid have studied CR-submanifolds of a trans-Sasakian manifold ([9],[10]). Recently, Lorentzian trans-Sasakian manifolds were st...