scholarly journals Doubly warped products with harmonic Weyl conformal curvature tensor

1994 ◽  
Vol 67 (1) ◽  
pp. 73-89 ◽  
Author(s):  
Andrzej Gębarowski
Keyword(s):  
Curvature Tensor ◽  
Warped Products ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Weyl Conformal Curvature Tensor

scholarly journals Pseudosymmetry properties of generalised Wintgen ideal Legendrian submanifolds

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1209-1215
Author(s):  
Aleksandar Sebekovic ◽  
Miroslava Petrovic-Torgasev ◽  
Anica Pantic
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Space Forms ◽  
Equality Case ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Sasakian Space Forms ◽  
Legendrian Submanifold ◽  
Legendrian Submanifolds ◽  
Weyl Conformal Curvature Tensor

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.

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 CONFORMALLY OSSERMAN MANIFOLDS AND CONFORMALLY COMPLEX SPACE FORMS

2004 ◽  
Vol 01 (01n02) ◽  
pp. 97-106 ◽  
Author(s):  
N. BLAŽIĆ ◽  
P. GILKEY
Keyword(s):  
Curvature Tensor ◽  
Complex Space ◽  
Jacobi Operator ◽  
Space Forms ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Weyl Curvature Tensor ◽  
Complex Space Forms ◽  
Weyl Conformal Curvature Tensor ◽  
Complex Projective

We characterize manifolds which are locally conformally equivalent to either complex projective space or to its negative curvature dual in terms of their Weyl curvature tensor. As a byproduct of this investigation, we classify the conformally complex space forms if the dimension is at least 8. We also study when the Jacobi operator associated to the Weyl conformal curvature tensor of a Riemannian manifold has constant eigenvalues on the bundle of unit tangent vectors and classify such manifolds which are not conformally flat in dimensions congruent to 2 mod 4.

scholarly journals On the intrinsic Deszcz symmetries and the extrinsic Chen character of Wintgen ideal submanifolds

2010 ◽  
Vol 41 (2) ◽  
pp. 109-116 ◽  
Author(s):  
S. Decu ◽  
M. Petrovic-Torgasev ◽  
A. Sebekovic ◽  
L. Verstraelen
Keyword(s):  
Ricci Curvature ◽  
Curvature Tensor ◽  
Real Space ◽  
Space Forms ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Real Space Forms ◽  
Wintgen Ideal Submanifolds ◽  
Weyl Conformal Curvature Tensor

In this paper it is shown that all Wintgen ideal submanifolds in ambient real space forms are Chen submanifolds. It is also shown that the Wintgen ideal submanifolds of dimension $ >3 $ in real space forms do intrinsically enjoy some curvature symmetries in the sense of Deszcz of their Riemann--Christoffel curvature tensor, of their Ricci curvature tensor and of their Weyl conformal curvature tensor.

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.

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