scholarly journals Traceless component of the conformal curvature tensor in Kähler manifold

2006 ◽  
Vol 56 (3) ◽  
pp. 857-874 ◽  
Author(s):  
S. Funabashi ◽  
H. S. Kim ◽  
Y.-M. Kim ◽  
J. S. Pak
Keyword(s):  
Curvature Tensor ◽  
Kähler Manifold ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Kahler Manifold

scholarly journals F-TRACELESS COMPONENT OF THE CONFORMAL CURVATURE TENSOR ON KÄHLER MANIFOLD

2007 ◽  
Vol 44 (4) ◽  
pp. 795-806
Author(s):  
Shoichi Funabashi ◽  
Hang-Sook Kim ◽  
Young-Mi Kim ◽  
Jin-Suk Pak
Keyword(s):  
Curvature Tensor ◽  
Kähler Manifold ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Kahler Manifold

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 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 On conformally recurrent spaces of second order

1969 ◽  
Vol 10 (1-2) ◽  
pp. 155-161 ◽  
Author(s):  
M. C. Chaki ◽  
A. N. Roy Chowdhury
Keyword(s):  
Curvature Tensor ◽  
Second Order ◽  
Covariant Differentiation ◽  
Metric Tensor ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Image Position ◽  
Conformally Recurrent ◽  
Zero Vector ◽  
Riemannian Spaces

In a recent paper [1] Adati and Miyazawa studied conformally recurrent spaces, that is, Riemannian spaces defined by where is the conformal curvature tensor: λi is a non-zero vector and comma denotes covariant differentiation with respect to the metric tensor gij.

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