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 On B- Covariant Derivative of First Order for Some Tensors in different Spaces

2021 ◽  
Vol 2 (2) ◽  
pp. 30-37
Author(s):  
Alaa A. Abdallah ◽  
A. A. Navlekar ◽  
Kirtiwant P. Ghadle
Keyword(s):  
Curvature Tensor ◽  
Covariant Derivative ◽  
Torsion Tensor ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
First Order ◽  
Recurrence Property ◽  
Necessary And Sufficient ◽  
The Relationship

In this paper, we study the relationship between Cartan's second curvature tensor $P_{jkh}^{i}$ and $(h) hv-$torsion tensor $C_{jk}^{i}$ in sense of Berwald. Moreover, we discuss the necessary and sufficient condition for some tensors which satisfy a recurrence property in $BC$-$RF_{n}$, $P2$-Like-$BC$-$RF_{n}$, $P^{\ast }$-$BC$-$RF_{n}$ and $P$-reducible-$BC-RF_{n}$.

scholarly journals On endo curvature tensor of a contact metric manifold

2008 ◽  
Vol 39 (2) ◽  
pp. 177-186
Author(s):  
Mohit Kumar Dwivedi ◽  
Jae-Bok Jun ◽  
Mukut Mani Tripathi
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Sasakian Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Contact Metric Manifold ◽  
Necessary And Sufficient

We prove that a $ ( k ,\mu ) $-manifold with vanishing Endo curvature tensor is a Sasakian manifold. We find a necessary and sufficient condition for a non-Sasakian $ ( k ,\mu ) $-manifold %$M$ whose Endo curvature tensor $ B^{es} $ satisfies $ B^{es}(\xi ,X) \cdot S=0 $, where $S$ is the Ricci tensor. Using $ {\cal D} $-homothetic deformation we obtain an example of an $ N\left( k\right) $-contact metric manifold on which $ B^{es}(\xi ,X)\cdot S\neq 0 $.

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.

On An Affine Connection Which Admits A Volume-Like Form

1990 ◽  
Vol 33 (4) ◽  
pp. 482-488 ◽  
Author(s):  
D. P. Chi ◽  
Y. D. Yoon
Keyword(s):  
Affine Connection ◽  
Riemannian Metric ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Riemannian Connection ◽  
Cech Cohomology ◽  
Necessary And Sufficient

AbstractA necessary and sufficient condition to obtain a volumelike form from an affine connection is given in terms of the Čech cohomology, after the volume-like form is naturally defined without a Riemannian metric. A necessary condition for an affine connection to be a Riemannian connection for some metric is also given.

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 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.

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