scholarly journals Homogeneity of Lorentzian three-manifolds with recurrent curvature

2013 ◽  
Vol 287 (1) ◽  
pp. 32-47 ◽  
Author(s):  
Eduardo García-Río ◽  
Peter B. Gilkey ◽  
Stana Nikčević
Keyword(s):  
Recurrent Curvature

scholarly journals Recurrent tensors and holonomy group

1974 ◽  
Vol 10 (1) ◽  
pp. 71-77 ◽  
Author(s):  
D.K. Datta
Keyword(s):  
Riemannian Manifold ◽  
Closed Form ◽  
Holonomy Group ◽  
Exact Form ◽  
Recurrent Curvature

Let M be a connected C∞. A method is being introduced here to study the action of the holonomy group and the restricted holonomy group of Γ on a recurrent tensor. The main result of this paper is that if the recurrence covector W of a recurrent tensor S on M is an exact form then the tensor S is invariant under the holonomy group of Γ and if W is a closed form then S is invariant under the restricted holonomy group of Γ. In the last section, this result is applied to some particular cases including the case of a riemannian manifold with recurrent curvature.

scholarly journals Kahlerian manifolds related in H-projective recurrent curvature killing vector fields with vectorial fields

2021 ◽  
Vol 9 (4) ◽  
pp. 435-440
Keyword(s):  
Vector Fields ◽  
Killing Vector ◽  
Complex Structures ◽  
Killing Vector Fields ◽  
Geometrical Properties ◽  
Projective Transformations ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Recurrent Curvature ◽  
Kählerian Manifolds

Izumi and Kazanari [2], has calculated and defined on infinitesimal holomorphically projective transformations in compact Kaehlerian manifolds. Also, Malave Guzman [3], has been studied transformations holomorphic ammeters projective equivalentes. After that, Negi [5], have studied and considered some problems concerning Pseudo-analytic vectors on Pseudo-Kaehlerian Manifolds. Again, Negi, et. al. [6],has defined and obtained an analytic HP-transformation in almost Kaehlerian spaces. In this paper we have measured and calculated a Kahlerian manifolds related in H-projective recurrent curvature killing vector fields with vectorial fields and their holomorphic propertiesEinsteinian and the constant curvature manifoldsare established.Kaehlerian holomorphically projective recurrent curvature manifolds with almost complex structures by using the geometrical properties of the harmonic and scalar curvatures calculated overkilling vectorial fieldsare obtained

scholarly journals Recurrent equiaffine projective Euclidean spaces

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1053-1058
Author(s):  
Almazbek Sabykanov ◽  
Josef Mikes ◽  
Patrik Peska
Keyword(s):  
Euclidean Space ◽  
Curvature Tensor ◽  
Ricci Tensor ◽  
Euclidean Spaces ◽  
Recurrent Curvature

In this paper, we study n-dimensional recurrent equiaffine projective Euclidean manifolds, i.e. manifolds with absolute recurrent curvature tensor, which admit geodesic mappings onto Euclidean space, and they are equiaffine (where was obtained the symmetric Ricci tensor). We obtained main conditions of recurrent projective Euclidean spaces and constructed their examples.

On Y. C. Wong's Conjecture

1970 ◽  
Vol 13 (4) ◽  
pp. 423-424
Author(s):  
D. K. Datta
Keyword(s):  
Curvature Tensor ◽  
Covariant Derivative ◽  
Linear Connection ◽  
Image Position ◽  
Recurrent Curvature

Let M be an n-dimensional connected C∞ manifold with a linear connection Γ. M is said to be of recurrent curvature with respect to Γ if the corresponding curvature tensor R satisfies [1], [4]where Δ denotes covariant derivative with respect to Γ and W is a nonzero covector called the recurrence co-vector. Let T be the torsion of Γ.

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