Quasi-conformal Curvature Tensor Research Articles

Generalized quasi-conformal curvature tensor and the spacetime of general relativity

In this paper, a study of generalized quasi-conformal curvature tensor has been made on the four dimensional spacetime of general relativity. Some results related to the application of such spacetime in the general relativity are obtained. Perfect fluid and dust fluid cosmological models have also been studied.

On Almost C(α)-Manifold Satisfying Certain Curvature Conditions

This research article is about the geometry of the almost C(α)- manifold. Some important properties of the almost C(α)- manifold with respect to the W_3- curvature tensor, such as W_3-flat and W_3- semi-symmetry, are investigated. The relationship of W_3- curvature tensor with Riemann, Ricci, projective, concircular and quasi-conformal curvature tensor is discussed on the almost C(α)- manifold and many important results are obtained. In addition, W_3- pseudo symmetry and W_3- Ricci pseudo symmetry are investigated for the almost C(α)- manifold. The results obtained are interesting and give an idea about the geometry of the almost C(α)- manifold.

Conformal η-Ricci soliton in Lorentzian para Kenmotsu manifolds

The objective of the present paper is to study conformal η-Ricci soliton on Lorentzian Para-Kenmotsu manifolds with some curvature conditions. We study Concircular curvature tensor, Quasi conformal curvature tensor, Codazi type of Ricci tensor and cyclic parallel Ricci tensor in Lorentzian Para-Kenmotsu manifolds. At last we give examples of such manifolds.

Some Curvature Properties of Normal Paracontact Metric Manifolds

The object of the present paper is to study curvature properties of a normal paracontact metric manifold with constant sectional curvature satisfying the conditions Z(ξ, X)R = 0, Z(ξ, X)P = 0, Z(ξ, X)Z = 0, Z(ξ, X)S = 0 and Z(ξ, X)C = 0. According to these cases, we classified normal paracontact metric manifolds, where R is the Riemanniann curvature tensor, C is the quasi-conformal curvature tensor, P is the projective curvature tensor, Z is the concircular curvature tensor and is the Ricci tensor.

Kontakt Metrik Çiftler Üzerinde Genelleştirilmiş Quasi-Conformal Eğrilik Tensörü

The aim of this paper is to examine normal metric contact pair (NMCP) manifolds under the flatness conditions ongeneralized quasi-conformal (GQC) curvature tensor. It is interested to classify GQC-flat and GQC-Z-flat NMCPmanifolds. We prove that a GQC-flat NMCP manifold is a generalized quasi-Einstein (GQE) manifold and also, suchmanifolds are the space of generalized quasi-constant curvature. Finally, we consider the sectional curvature of NMCPmanifolds under the flatness conditions of GQC curvature tensor.

On Quasi-Conformal Flat Para-Sasakian Manifolds

In this paper, we present some new results on invariant submanifolds of a para-Sasakian manifold under the quasi-conformally flatness condition. Firstly, we examine flatness of quasi-conformal curvature tensor on para-Sasakian manifolds. We prove that a quasi-conformally flat para-Sasakian manifold is an $ \eta $-Einstein manifold. Also, we give some results on the sectional curvature of such manifolds. Secondly, we consider the invariant submanifolds of a quasi-conformally flat para-Sasakian manifold. We prove that a totally umbilical submanifold of a para-Sasakian manifold is invariant. In addition, we investigate curvature properties of such submanifolds and we show that a totally umbilical invariant submanifold of a quasi-conformally flat para-Sasakian manifold is an $ \eta $-Einstein manifold. Finally, we work on the sectional curvature properties of an invariant submanifold of a quasi-conformally flat para-Sasakian manifold.

Some curvature properties on Lorentzian $\beta$-Kenmotsu manifold with a semi-symmetric semi-metric connection

The object of the present paper is to study quasi conformal curvature tensor and conformal curvature tensor on Lorentzian $\beta$-Kenmotsu manifold with a semi-symmetric semi-metric connection. Moreover, we consider quasi conformally flat, $\xi$-quasi conformally flat, $\phi$-conformally semisymmetric and conformally flat Lorentzian $\beta$-Kenmotsu manifold with a semi-symmetric semi-metric connection and obtain the scalar curvature $r$ in each case.

QUASI-CONFORMAL CURVATURE TENSOR OF GENERALIZED SASAKIAN-SPACE-FORMS

The present paper deals the study of generalised Sasakian-space-forms with the conditions Cq(ξ,X).S = 0, Cq(ξ,X).R = 0 and Cq(ξ,X).Cq = 0, where R, S and Cq denote Riemannian curvature tensor, Ricci tensor and quasi-conformal curvature tensor of the space-form, respectively and at last, we have given some examples to improve our results.

Perfect fluid spacetimes with harmonic generalized curvature tensor

We show that $n$-dimensional perfect fluid spacetimes with diver\-gen\-ce-free conformal curvature tensor and constant scalar curvature are generalized Robertson Walker (GRW) spacetimes; as a consequence a perfect fluid Yang pure space is a GRW spacetime. We also prove that perfect fluid spacetimes with harmonic generalized curvature tensor are, under certain conditions, GRW spacetimes. As particular cases, perfect fluids with divergence-free projective, concircular, conharmonic or quasi-conformal curvature tensor are GRW spacetimes. Finally, we explore some physical consequences of such results.

Some characterizations of Lorentzian manifolds

Generalized Robertson–Walker (GRW) spacetime is the generalization of the Robertson–Walker (RW) spacetime and a further generalization of GRW spacetime is the twisted spacetime. In this paper, we generalize the results of the paper [C. A. Mantica, Y. J. Suh and U. C. De, A note on generalized Robertson–Walker spacetimes, Int. J. Geom. Methods Mod. Phys. 13 (2016), Article Id: 1650079, 9 pp., doi: 101142/s0219887816500791 ]. We prove that a Ricci simple Lorentzian manifold with vanishing quasi-conformal curvature tensor is a RW spacetime. Further, we prove that a Ricci simple Lorentzian manifold with harmonic quasi-conformal curvature tensor is a GRW spacetime. As a consequence, we obtain several corollaries. Finally, we have cited some examples of the obtained results.

On the quasi-conformal curvature tensor of an almost Kenmotsu manifold with nullity distributions

The object of the present paper is to characterize quasi-conformally flat and $\xi$-quasi-conformally flat almost Kenmotsu manifolds with $(k,\mu)$-nullity and $(k,\mu)'$-nullity distributions respectively. Also we characterize almost Kenmotsu manifolds with vanishing extended quasi-conformal curvature tensor and extended $\xi$-quasi-conformally flat almost Kenmotsu manifolds such that the characteristic vector field $\xi$ belongs to the $(k,\mu)$-nullity distribution.

QUASI-CONFORMAL CURVATURE TENSOR ON SASAKIAN MANIFOLDS

In this paper we studied some curvature properties of quasi-conformal curvature tensor on Sasakian manifolds. We have proven that a -dimensional Sasakian manifold satisfying the curvature conditions and is an Einstein manifold. We have also obtained some results on quasi-conformally recurrent Sasakian manifold. Finally, Sasakian manifold satisfying the condition was studied. 12n 0 ., S Y XR0 ., W Y XR0 divWJournal of Institute of Science and TechnologyVolume 22, Issue 1, July 2017, Page: 94-98

Ricci solitons in Sasakian manifold

Recently the present author introduced the notion of generalized quasi-conformal curvature tensor which bridges conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor. The object of the present paper is to find out curvature conditions for which Ricci solitons in Sasakian manifolds are sometimes shrinking and some other time remain expanding.

Quasi-conformal curvature tensor with respect to a semi-symmetric non-metric connection in a Kenmotsu manifold

AbstractThe objective of the present paper is to study some new results on quasi-conformal curvature tensor in a Kenmotsu manifold with respect to a semi-symmetric non-metric connection.

Deszcz Pseudo Symmetry Type LP-Sasakian Manifolds

Abstract Recently the present authors introduced the notion of generalized quasi-conformal curvature tensor which bridges Conformal curvature tensor, Concircular curvature tensor, Projective curvature tensor and Conharmonic curvature tensor. This paper attempts to charectrize LP-Sasakian manifolds with ω(X, Y) · 𝒲 = L{(X ∧ ɡ Y) · 𝒲}. On the basis of this curvature conditions and by taking into account, the permutation of different curvature tensors we obtained and tabled the nature of the Ricci tensor for the respective pseudo symmetry type LP-Sasakian manifolds.

ON GENERALIZED QUASI-CONFORMAL N(k, μ)-MANIFOLDS

The object of the present paper is to introduce a new curvature tensor, named generalized quasi-conformal curvature tensor which bridges conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor. Flatness and symmetric properties of generalized quasi-conformal curvature tensor are studied in the frame of (k, <TEX>${\mu}$</TEX>)-contact metric manifolds.

Some Curvature Properties of Kenmotsu Manifolds

In this paper we study quasiconformal curvature tensor and C-Bochner curvature tensor on Kenmotsu manifolds. We show that quasiconformal \(\phi \)-recurrent and globally \(\phi \)-quasiconformal Kenmotsu manifolds are Einstein manifolds. Some observations for quasiconformal \(\phi \)-recurrent and globally \(\phi \)-quasiconformal Kenmotsu manifolds are given.We also consider the conditions \(B(X,Y)Z=0\), \(B \cdot S=0\), \(B \cdot R=0\) and \(R \cdot B=0\) on a Kenmotsu manifold, where B is the C-Bochner curvature tensor.

On some classes of generalized quasi Einstein manifolds

In the present paper, we investigate generalized quasi Einstein manifolds satisfying some special curvature conditions R?S = 0,R?S = LSQ(g,S), C?S = 0,?C?S = 0,?W?S = 0 and W2?S = 0 where R, S, C,?C,?W and W2 respectively denote the Riemannian curvature tensor, Ricci tensor, conformal curvature tensor, concircular curvature tensor, quasi conformal curvature tensor and W2-curvature tensor. Later, we find some sufficient conditions for a generalized quasi Einstein manifold to be a quasi Einstein manifold and we show the existence of a nearly quasi Einstein manifolds, by constructing a non trivial example.

Curvature tensor of almost C(λ) manifolds

The present paper deals with certain characterization of curvature conditions on Pseudo-projective and Quasi-conformal curvature tensor on almost $C(\lambda)$ manifolds. The main object of the paper is to study the flatness of the Pseudo-projective, Quasi-conformal curvature tensor, $\xi$-Pseudo-projective, $\xi$-Quasi-conformal curvature tensor on almost $C(\lambda)$ manifolds.

Properties of the quasi-conformal curvature tensor of Kähler-Norden manifolds

The object of the present paper is to study quasi-conformally flat and parallel quasi-conformal curvature tensor of a Kähler-Norden manifold. Besides this we also study quasi-conformally semisymetric Kähler-Norden manifolds. Finally, we mention an example to verify a Theorem of our paper.