scholarly journals On concircular transformations in Riemannian spaces

1986 ◽  
Vol 40 (2) ◽  
pp. 218-225 ◽  
Author(s):  
Luo Chongshan
Keyword(s):  
Symmetric Space ◽  
Curvature Tensor ◽  
Constant Curvature ◽  
Riemannian Space ◽  
Symmetric Spaces ◽  
Riemannian Curvature ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Riemannian Curvature Tensor ◽  
Concircular Transformation

AbstractThis paper introduces a tensor that contains the Riemannian curvature tensor and the conformal curvature tensor as special examples in the Riemannian space (Mn, g), and by using this tensor we define C-semi-symmetric space. In this paper, we have the following main result: if there is a non-trivial concircular transformation between two C-semi-symmetric spaces, then both spaces are of quasi-constant curvature.

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

2020 ◽  
Vol 35 (1) ◽  
pp. 089
Author(s):  
Braj B. Chaturvedi ◽  
Brijesh K. Gupta
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Space Form ◽  
Riemannian Curvature ◽  
Space Forms ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Sasakian Space Forms ◽  
Riemannian Curvature Tensor

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.

scholarly journals On some classes of generalized quasi Einstein manifolds

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 443-456 ◽  
Author(s):  
Sinem Güler ◽  
Sezgin Demirbağ
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Einstein Manifold ◽  
Sufficient Conditions ◽  
Riemannian Curvature ◽  
Einstein Manifolds ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Riemannian Curvature Tensor ◽  
Concircular Curvature Tensor

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.

scholarly journals Conformal curvature tensors in a generalized Riemannian space in Eisenhart sense

2020 ◽  
pp. 34-34
Author(s):  
Ana Velimirovic
Keyword(s):  
Curvature Tensor ◽  
Riemannian Space ◽  
Conformal Transformation ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Generalized Riemannian Space ◽  
Curvature Tensors ◽  
Special Case

In the present paper generalizations of conformal curvature tensor from Riemannian space are given for five independent curvature tensors in generalized Riemannian space (GRN ), i.e. when the basic tensor is non-symmetric. In earlier works of S. Mincic and M. Zlatanovic et al a special case has been investigated, that is the case when in the conformal transformation the torsion remains invariant (equitorsion transformation). In the present paper this condition is not supposed and for that reason the results are more general and new.

scholarly journals Some invariants of conformal mappings of a generalized Riemannian space

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1465-1474
Author(s):  
Nenad Vesic
Keyword(s):  
Curvature Tensor ◽  
Riemannian Space ◽  
Affine Connection ◽  
Conformal Mappings ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Necessary And Sufficient ◽  
Weyl Conformal Curvature Tensor

Invariants of conformal mappings between non-symmetric affine connection spaces are obtained in this paper. Correlations between these invariants and the Weyl conformal curvature tensor are established. Before these invariants, it is obtained a necessary and sufficient condition for a mapping to be conformal. Some appurtenant invariants of conformal mappings are obtained.

scholarly journals A new curvaturelike tensor field in an almost contact Riemannian manifold II

2018 ◽  
Vol 103 (117) ◽  
pp. 113-128 ◽  
Author(s):  
Koji Matsumoto
Keyword(s):  
Riemannian Manifold ◽  
Curvature Tensor ◽  
Tensor Field ◽  
Sasakian Manifold ◽  
Tensor Fields ◽  
Geometrical Properties ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Riemannian Curvature Tensor ◽  
Contact Riemannian Manifold

In the last paper, we introduced a new curvaturlike tensor field in an almost contact Riemannian manifold and we showed some geometrical properties of this tensor field in a Kenmotsu and a Sasakian manifold. In this paper, we define another new curvaturelike tensor field, named (CHR)3-curvature tensor in an almost contact Riemannian manifold which is called a contact holomorphic Riemannian curvature tensor of the second type. Then, using this tensor, we mainly research (CHR)3-curvature tensor in a Sasakian manifold. Then we define the notion of the flatness of a (CHR)3-curvature tensor and we show that a Sasakian manifold with a flat (CHR)3-curvature tensor is flat. Next, we introduce the notion of (CHR)3-?-Einstein in an almost contact Riemannian manifold. In particular, we show that Sasakian (CHR)3- ?-Einstein manifold is ?-Einstain. Moreover, we define the notion of (CHR)3- space form and consider this in a Sasakian manifold. Finally, we consider a conformal transformation of an almost contact Riemannian manifold and we get new invariant tensor fields (not the conformal curvature tensor) under this transformation. Finally, we prove that a conformally (CHR)3-flat Sasakian manifold does not exist.

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

2018 ◽  
Vol 33 (2) ◽  
pp. 255
Author(s):  
Dibakar Dey ◽  
Pradip Majhi
Keyword(s):  
Vector Field ◽  
Curvature Tensor ◽  
Conformally Flat ◽  
Kenmotsu Manifold ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Nullity Distribution ◽  
Characteristic Vector Field

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.

A note on generalized Robertson–Walker space-times

2016 ◽  
Vol 13 (06) ◽  
pp. 1650079 ◽  
Author(s):  
Carlo Alberto Mantica ◽  
Young Jin Suh ◽  
Uday Chand De
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Perfect Fluid ◽  
Curvature Tensor ◽  
Weyl Tensor ◽  
Space Time ◽  
Stiff Matter ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Mass Less Scalar Field

A generalized Robertson–Walker (GRW) space-time is the generalization of the classical Robertson–Walker space-time. In the present paper, we show that a Ricci simple manifold with vanishing divergence of the conformal curvature tensor admits a proper concircular vector field and it is necessarily a GRW space-time. Further, we show that a stiff matter perfect fluid space-time or a mass-less scalar field with time-like gradient and with divergence-free Weyl tensor are GRW space-times.

scholarly journals On projective-symmetric spaces

1964 ◽  
Vol 4 (1) ◽  
pp. 113-121 ◽  
Author(s):  
Bandana Gupta
Keyword(s):  
Symmetric Space ◽  
Curvature Tensor ◽  
Symmetric Spaces ◽  
Covariant Differentiation ◽  
Metric Tensor ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Image Position ◽  
Riemannian Spaces

This paper deals with a type of Remannian space Vn (n ≧ 2) for which the first covariant dervative of Weyl's projective curvature tensor is everywhere zero, that is where comma denotes covariant differentiation with respect to the metric tensor gij of Vn. Such a space has been called a projective-symmetric space by Gy. Soós [1]. We shall denote such an n-space by ψn. It will be proved in this paper that decomposable Projective-Symmetric spaces are symmetric in the sense of Cartan. In sections 3, 4 and 5 non-decomposable spaces of this kind will be considered in relation to other well-known classes of Riemannian spaces defined by curvature restrictions. In the last section the question of the existence of fields of concurrent directions in a ψ will be discussed.

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