conformal curvature tensor
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2021 ◽  
Vol 10 (4) ◽  
pp. 1969-1982
Author(s):  
B. P. Murthy ◽  
R. T. Naveen Kumar ◽  
P. S. K. Reddy ◽  
Venkatesha


Author(s):  
Sabina Eyasmin

The hypersurface of a space is one of the most important objects in a space. Many authors studied the various geometric aspects of hypersurfaces in a space form. The notion of conformal flatness is one of the most primitive concepts in differential geometry. Again, conformally flat space is a proper generalization of a space form. In this paper, we study the geometry of hypersurfaces in a conformally flat manifold. Then we have investigated some sufficient conditions imposed on the shape operator for which the hypersurface satisfies various pseudosymmetric-type conditions imposed on its conformal curvature tensor.



Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 657-666
Author(s):  
Young Suh ◽  
Vasant Chavan ◽  
Naeem Pundeer

In the present paper, we carried out a systematic investigation of pseudo-quasi-conformal curvature tensor has been made on the four-dimensional spacetime of general relativity. The spacetime fulfilling Einstein?s field equations with vanishing of pseudo-quasi-conformal curvature tensor is being considered and existence of Killing and conformal Killing vectors on such spacetime have been established. At last, we extend the similar case for the investigation of cosmological models with dust and perfect fluid spacetime.



2020 ◽  
Vol 35 (1) ◽  
pp. 089
Author(s):  
Braj B. Chaturvedi ◽  
Brijesh K. Gupta

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.



Author(s):  
Ana Velimirovic

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.



2019 ◽  
Vol 22 (1) ◽  
pp. 13-28
Author(s):  
P. Somashekhara ◽  
Venkatesha ◽  
R. T. Naveen Kumar


Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1209-1215
Author(s):  
Aleksandar Sebekovic ◽  
Miroslava Petrovic-Torgasev ◽  
Anica Pantic

For Legendrian submanifolds Mn in Sasakian space forms ?M2n+1(c), I. Mihai obtained an inequality relating the normalised scalar curvature (intrinsic invariant) and the squared mean curvature and the normalised scalar normal curvature of M in the ambient space ?M (extrinsic invariants) which is called the generalised Wintgen inequality, characterising also the corresponding equality case. And a Legendrian submanifold Mn in Sasakian space forms ?M2n+1(c) is said to be generalised Wintgen ideal Legendrian submanifold of ?M2n+1(c) when it realises at everyone of its points the equality in such inequality. Characterisations based on some basic intrinsic symmetries involving the Riemann-Cristoffel curvature tensor, the Ricci tensor and the Weyl conformal curvature tensor belonging to the class of pseudosymmetries in the sense of Deszcz of such generalised Wintgen ideal Legendrian submanifolds are given.



2019 ◽  
Vol 16 (01) ◽  
pp. 1950016
Author(s):  
Uday Chand De ◽  
Young Jin Suh

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.



OALib ◽  
2019 ◽  
Vol 06 (06) ◽  
pp. 1-7
Author(s):  
Basavaraju Phalaksha Murthy ◽  
Venkatesha Venkatesha


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