M-projective curvature tensor on an (LCS)2n+1-manifold

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
B. Shanmukha ◽  
V. Venkatesha
Keyword(s):  
Curvature Tensor ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Curvature Tensors

Abstract In this paper, we study M-projective curvature tensors on an ( LCS ) 2 ⁢ n + 1 {(\mathrm{LCS})_{2n+1}} -manifold. Here we study M-projectively Ricci symmetric and M-projectively flat admitting spacetime.

On M-Projective Curvature Tensor of Lorentzian α-Sasakian Manifolds

2017 ◽  
Vol 18 ◽  
pp. 22-31
Author(s):  
D.G. Prakasha ◽  
Vasant Chavan
Keyword(s):  
Curvature Tensor ◽  
Unit Sphere ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Projective Curvature Tensor

In this paper, we study the nature of Lorentzianα-Sasakian manifolds admitting M-projective curvature tensor. We show that M-projectively flat and irrotational M-projective curvature tensor of Lorentzian α-Sasakian manifolds are locally isometric to unit sphere Sn(c) , wherec = α2. Next we study Lorentzianα-Sasakian manifold with conservative M-projective curvature tensor. Finally, we find certain geometrical results if the Lorentzianα-Sasakian manifold satisfying the relation M(X,Y)⋅R=0.

Some curvature restricted geometric structures for projective curvature tensors

2018 ◽  
Vol 15 (09) ◽  
pp. 1850157 ◽  
Author(s):  
Absos Ali Shaikh ◽  
Haradhan Kundu
Keyword(s):  
Curvature Tensor ◽  
Riemannian Manifolds ◽  
Einstein Manifolds ◽  
Geometric Structures ◽  
Projective Curvature ◽  
Riemannian Case ◽  
Projective Curvature Tensor ◽  
Projective Operator ◽  
Curvature Tensors

The projective curvature tensor is an invariant under geodesic preserving transformations on semi-Riemannian manifolds. It possesses different geometric properties than other generalized curvature tensors. The main object of the present paper is to study some semisymmetric type and pseudosymmetric type curvature restricted geometric structures due to projective curvature tensor. The reduced pseudosymmetric type structures for various Walker type conditions are deduced and the existence of Venzi space is ensured. It is shown that the geometric structures formed by imposing projective operator on a (0,4)-tensor is different from that for the corresponding (1,3)-tensor. Characterization of various semisymmetric type and pseudosymmetric type curvature restricted geometric structures due to projective curvature tensor are obtained on semi-Riemannian manifolds, and it is shown that some of them reduce to Einstein manifolds for the Riemannian case. Finally, to support our theorems, four suitable examples are presented.

The ℳ-projective curvature tensor field on generalized (κ,μ)-paracontact metric manifolds

2020 ◽  
Vol 27 (1) ◽  
pp. 141-147 ◽  
Author(s):  
Doddabhadrappla G. Prakasha ◽  
Luis M. Fernández ◽  
Kakasab Mirji
Keyword(s):  
Curvature Tensor ◽  
Tensor Field ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Projective Curvature Tensor

AbstractWe consider generalized {(\kappa,\mu)}-paracontact metric manifolds satisfying certain flatness conditions on the {\mathcal{M}}-projective curvature tensor. Specifically, we study ξ-{\mathcal{M}}-projectively flat and {\mathcal{M}}-projectively flat generalized {(\kappa,\mu)}-paracontact metric manifolds and, further, ϕ-{\mathcal{M}}-projectively symmetric generalized {(\kappa\neq-1,\mu)}-paracontact metric manifolds. We prove that they are characterized by certain structures whose properties are discussed in some detail.

η-Einstein nearly Kenmotsu manifolds

2019 ◽  
Vol 12 (06) ◽  
pp. 2040010 ◽  
Author(s):  
Pelin Tekin ◽  
Nesip Aktan
Keyword(s):  
Scalar Curvature ◽  
Curvature Tensor ◽  
Kenmotsu Manifold ◽  
Projectively Flat ◽  
Kenmotsu Manifolds ◽  
Projective Curvature ◽  
Conharmonic Curvature Tensor ◽  
Projective Curvature Tensor ◽  
Tensor Formula

In this paper, we showed that an [Formula: see text]-Einstein nearly Kenmotsu manifold with projective curvature tensor [Formula: see text], and conharmonic curvature tensor [Formula: see text], satisfy the conditions [Formula: see text] and [Formula: see text], respectively. Furthermore, we obtain scalar curvature of a projectively flat and a conharmonically flat [Formula: see text]-Einstein nearly Kenmotsu manifold.

scholarly journals Projective Curvature Tensor with Respect to Zamkovoy Connection in Lorentzian Para-Sasakian Manifolds

2020 ◽  
Vol 26 (3) ◽  
pp. 369-379
Author(s):  
Abhijit Mandal ◽  
Ashoke Das
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Curvature Tensors

The purpose of the present paper is to study some properties of the Projective curvature tensor with respect to Zamkovoy connection in Lorentzian Para Sasakian manifold(or,LP-Sasakian manifold)'And we have studied some results in Lorentzian Para-Sasakian manifold with the help of Zamkovoy connection and Projective curvature tensor.Also we discussed the LP-Sasakian manifold satisfying P*(ξ,U)∘W₀*=0,P*(ξ,U)∘W₂*=0 , where W₀*,W₂* and P* are W₀,W₂ and Projective curvature tensors with respect to Zamkovoy connection.

scholarly journals Generalized para-Kähler spaces in Eisenhart’s sense admitting a holomorphically projective mapping

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4001-4012
Author(s):  
Milos Petrovic
Keyword(s):  
Curvature Tensor ◽  
Product Structure ◽  
Projective Mapping ◽  
Almost Product Structure ◽  
Projective Curvature ◽  
Geometric Objects ◽  
Projective Curvature Tensor ◽  
Curvature Tensors

We relax the conditions related to the almost product structure and in such a way introduce a wider class of generalized para-K?hler spaces. Some properties of the curvature tensors as well as those of the corresponding Ricci tensors of these spaces are pointed out. We consider holomorphically projective mappings between generalized para-K?hler spaces in Eisenhart?s sense. Also, we examine some invariant geometric objects with respect to equitorsion holomorphically projective mappings. These geometric objects reduce to the para-holomorphic projective curvature tensor in case of holomorphically projective mappings between usual para-K?hler spaces.

scholarly journals ON m-PROJECTIVE CURVATURE TENSOR OF GENERALIZED SASAKIAN-SPACE-FORMS

2018 ◽  
pp. 361
Author(s):  
Shravan K. Pandey ◽  
R.N. Singh
Keyword(s):  
Curvature Tensor ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Projective Curvature Tensor

\begin{abstract}The object of the present paper is to characterize generalized Sasakian-space-forms satisfying certain curvature conditions on m-projective curvature tensor. In this paper, we study m-projectively semisymmetric, m-projectively flat, $\xi$-m-projectively flat, m-projectively recurrent generalized Sasakian-space-forms. Also $W^*.S = 0$ and $W^*.R= 0$ on generalized Sasakian-space-forms are studied.\end{abstract}

scholarly journals ∗-Conformal η-Ricci soliton on Sasakian manifold

2021 ◽  
pp. 2250035
Author(s):  
Soumendu Roy ◽  
Santu Dey ◽  
Arindam Bhattacharyya ◽  
Shyamal Kumar Hui
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifold ◽  
Ricci Soliton ◽  
Sasakian Manifolds ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Projective Curvature Tensor

In this paper, we study ∗-Conformal [Formula: see text]-Ricci soliton on Sasakian manifolds. Here, we discuss some curvature properties on Sasakian manifold admitting ∗-Conformal [Formula: see text]-Ricci soliton. We obtain some significant results on ∗-Conformal [Formula: see text]-Ricci soliton in Sasakian manifolds satisfying [Formula: see text], [Formula: see text], [Formula: see text] [Formula: see text], where [Formula: see text] is Pseudo-projective curvature tensor. The conditions for ∗-Conformal [Formula: see text]-Ricci soliton on [Formula: see text]-conharmonically flat and [Formula: see text]-projectively flat Sasakian manifolds have been obtained in this paper. Lastly we give an example of five-dimensional Sasakian manifolds satisfying ∗-Conformal [Formula: see text]-Ricci soliton.

scholarly journals Deszcz Pseudo Symmetry Type LP-Sasakian Manifolds

2016 ◽  
Vol 54 (1) ◽  
pp. 35-53
Author(s):  
Kanak Kanti Baishya ◽  
Partha Roy Chowdhury
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Symmetry Type ◽  
Sasakian Manifolds ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Concircular Curvature Tensor ◽  
Curvature Tensors

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.

scholarly journals Generalized Sasakian-Space-Forms with Projective Curvature Tensor

2014 ◽  
Vol 47 (3) ◽  
Author(s):  
A. Sarkar ◽  
Ali Akbar
Keyword(s):  
Curvature Tensor ◽  
Sufficient Conditions ◽  
Space Forms ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Sasakian Space Forms ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Metric Connection ◽  
Projective Curvature Tensor

AbstractThe object of the present paper is to study Ф-projectively flat generalized Sasakian-space-forms, projectively locally symmetric generalized Sasakian-space-forms and projectively locally Ф-symmetric generalized Sasakian-space-forms. All the obtained results are in the form of necessary and sufficient conditions. Interesting relations between projective curvature tensor and conformal curvature tensor of a generalized Sasakian-spaceform of dimension greater than three have been established. Some of these properties are also analyzed in the light of quarter-symmetric metric connection, in addition with the Levi-Civita connection. Obtained results are supported by illustrative examples.

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