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ON GENERALIZED RICCI-RECURRENT TRANS-SASAKIAN MANIFOLDS
Kim, Jeong-Sik,Prasad, Rajendra,Tripathi, Mukut-Mani Korean Mathematical Society 2002 대한수학회지 Vol.39 No.6
Generalized Ricci-recurrent trans-Sasakian manifolds are studied. Among others, it is proved that a generalized Ricci-recurrent cosymplectic manifold is always recurrent Generalized Ricci-recurrent trans-Sasakian manifolds of dimension $\geq$ 5 are locally classified. It is also proved that if M is one of Sasakian, $\alpha$-Sasakian, Kenmotsu or $\beta$-Kenmotsu manifolds, which is gener-alized Ricci-recurrent with cyclic Ricci tensor and non-zero A (ξ) everywhere; then M is an Einstein manifold.
SASAKIAN STATISTICAL MANIFOLDS WITH QSM-CONNECTION AND THEIR SUBMANIFOLDS
( Sema Kazan ) 호남수학회 2023 호남수학학술지 Vol.45 No.3
In this present paper, we study QSM-connection (quartersymmetric metric connection) on Sasakian statistical manifolds. Firstly, we express the relation between the QSM-connection □ and the torsionfree connection ∇ and obtain the relation between the curvature tensors ~R of □ and R of ∇. After then we obtain these relations for □ and the dual connection ∇* of ∇. Also, we give the relations between the curvature tensor ~R of QSM-connection □ and the curvature tensors R and R* of the connections ∇ and ∇* on Sasakian statistical manifolds. We obtain the relations between the Ricci tensor of QSM-connection □ and the Ricci tensors of the connections ∇ and ∇*. After these, we construct an example of a 3-dimensional Sasakian manifold admitting the QSM-connection in order to verify our results. Finally, we study the submanifolds with the induced connection with respect to QSM-connection of statistical manifolds.
On Semiparallel and Weyl-semiparallel Hypersurfaces of Kaehler Manifolds
Ozgur, Cihan,Murathan, Cengizhan,Arslan, Kadri Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.1
We study on semiparallel and Weyl semiparallel Sasakian hypersurfaces of Kaehler manifolds. We prove that a (2n + 1)-dimensional Sasakian hypersurface M of a (2n+2)-dimensional Kaehler manifold $\widetilde{M}^{2n+2}$ is semiparallel if and only if it is totally umbilical with unit mean curvature, if dimM = 3 and $\widetilde{M}^4$ is a Calabi-Yau manifold, then $\widetilde{M}$ is flat at each point of M. We also prove that such a hypersurface M is Weyl-semiparallel if and only if it is either an ${\eta}$-Einstein manifold or semiparallel. We also investigate the extended classes of semiparallel and Weyl semiparallel Sasakian hypersurfaces of Kaehler manifolds.
TRANS-SASAKIAN MANIFOLDS WITH RESPECT TO GENERALIZED TANAKA-WEBSTER CONNECTION
Kazan, Ahmet,Karadag, H.Bayram The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.3
In this study, we use the generalized Tanaka-Webster connection on a trans-Sasakian manifold of type (${\alpha},{\beta}$) and obtain the curvature tensors of a trans-Sasakian manifold with respect to this connection. Also, we investigate some special curvature conditions of a trans-Sasakian manifold with respect to generalized Tanaka-Webster connection and finally, give an example for trans-Sasakian manifolds.
∗-RICCI SOLITONS AND ∗-GRADIENT RICCI SOLITONS ON 3-DIMENSIONAL TRANS-SASAKIAN MANIFOLDS
Dey, Dibakar,Majhi, Pradip Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.2
The object of the present paper is to characterize 3-dimensional trans-Sasakian manifolds of type (α, β) admitting ∗-Ricci solitons and ∗-gradient Ricci solitons. Under certain restrictions on the smooth functions α and β, we have proved that a trans-Sasakian 3-manifold of type (α, β) admitting a ∗-Ricci soliton reduces to a β-Kenmotsu manifold and admitting a ∗-gradient Ricci soliton is either flat or ∗-Einstein or it becomes a β-Kenmotsu manifold. Also an illustrative example is presented to verify our results.
Siddiqi, Mohammed Danish,Chaubey, Sudhakar Kumar,Ramandi, Ghodratallah Fasihi Department of Mathematics 2021 Kyungpook mathematical journal Vol.61 No.3
This paper examines the behavior of a 3-dimensional trans-Sasakian manifold equipped with a gradient generalized quasi-Yamabe soliton. In particular, It is shown that α-Sasakian, β-Kenmotsu and cosymplectic manifolds satisfy the gradient generalized quasi-Yamabe soliton equation. Furthermore, in the particular case when the potential vector field ζ of the quasi-Yamabe soliton is of gradient type ζ = grad(ψ), we derive a Poisson's equation from the quasi-Yamabe soliton equation. Also, we study harmonic aspects of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds sharing a harmonic potential function ψ. Finally, we observe that 3-dimensional compact trans-Sasakian manifold admits the gradient generalized almost quasi-Yamabe soliton with Hodge-de Rham potential ψ. This research ends with few examples of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds.
GOLDEN PARA-CONTACT METRIC MANIFOLDS
Beldjilali, Gherici,Bouzir, Habib Korean Mathematical Society 2022 대한수학회논문집 Vol.37 No.4
The purpose of the present paper is to introduce a new class of almost para-contact metric manifolds namely, Golden para-contact metric manifolds. Then, we are particularly interested in a more special type called Golden para-Sasakian manifolds, where we will study their fundamental properties and we present many examples which justify their study.
Transversal lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds
Shiv Sharma Shukla,Vipul Singh 대한수학회 2023 대한수학회논문집 Vol.38 No.4
In this paper, we introduce and study two new classes of lightlike submersions, called radical transversal and transversal lightlike submersions between an indefinite Sasakian manifold and a lightlike manifold. We give examples and investigate the geometry of distributions involved in the definitions of these lightlike submersions. We also study radical transversal and transversal lightlike submersions from an indefinite Sasakian manifold onto a lightlike manifold with totally contact umbilical fibers.
The Geometry of δ-Ricci-Yamabe Almost Solitons on Para contact Metric Manifolds
Somnath Mondal,Santu Dey,서영진,Arindam Bhattacharyya 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.4
In this article we study a δ-Ricci-Yamabe almost soliton within the framework of paracontact metric manifolds. In particular we study δ-Ricci-Yamabe almost soliton and gradient δ-Ricci-Yamabe almost soliton on K-paracontact and para-Sasakian manifolds. We prove that if a K-paracontact metric g represents a δ-Ricci-Yamabe almost soliton with the non-zero potential vector field V parallel to ξ, then g is Einstein with Einstein constant -2n. We also show that there are no para-Sasakian manifolds that admit a gra dient δ-Ricci-Yamabe almost soliton. We demonstrate a δ-Ricci-Yamabe almost soliton on a (κ, µ)-paracontact manifold.
ON A CLASS OF THREE-DIMENSIONAL TRANS-SASAKIAN MANIFOLDS
De, Uday Chand,De, Krishnendu Korean Mathematical Society 2012 대한수학회논문집 Vol.27 No.4
The object of the present paper is to study 3-dimensional trans-Sasakian manifolds with conservative curvature tensor and also 3-dimensional conformally flat trans-Sasakian manifolds. Next we consider compact connected $\eta$-Einstein 3-dimensional trans-Sasakian manifolds. Finally, an example of a 3-dimensional trans-Sasakian manifold is given, which verifies our results.