Codazzi Tensor Fields, Curvature and Pontryagin Forms

Derdziński, Andrzej; Chen, Shen

doi:10.1112/plms/s3-47.1.15

Cited by 70 publications

(68 citation statements)

References 12 publications

(19 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We recall that a (0, 2)-symmetric tensor B is said to be a Codazzi tensor if it satisfies the Codazzi equation, i.e. trivial if it is a constant multiple of the metric tensor [20]. We denote by B the class of semi-Riemannian manifolds with Ricci tensor S as Codazzi tensor, i.e.…”

Section: Manifolds With Cyclic Parallel and Codazzi Type Ricci Tensormentioning

confidence: 99%

Curvature properties of Gödel metric

Deszcz

Hotloś

Jełowicki

et al. 2014

Int. J. Geom. Methods Mod. Phys.

View full text Add to dashboard Cite

show abstract

Section: Manifolds With Cyclic Parallel and Codazzi Type Ricci Tensormentioning

confidence: 99%

Curvature properties of Gödel metric

Deszcz

Hotloś

Jełowicki

et al. 2014

Int. J. Geom. Methods Mod. Phys.

View full text Add to dashboard Cite

show abstract

“…The geometrical and topological consequences of the existence of a non-trivial Codazzi tensor on a Riemannian manifold have been studied by Derdzinski and Shen [3]. The simplest Codazzi tensors are parallel one.…”

Section: Divergence-free Concircular Curvature Tensor and Fluid Spacementioning

confidence: 98%

Concircular Curvature Tensor and Fluid Spacetimes

Ahsan

Siddiqui

2009

Int J Theor Phys

View full text Add to dashboard Cite

In the differential geometry of certain F -structures, the importance of concircular curvature tensor is very well known. The relativistic significance of this tensor has been explored here. The spacetimes satisfying Einstein field equations and with vanishing concircular curvature tensor are considered and the existence of Killing and conformal Killing vectors have been established for such spacetimes. Perfect fluid spacetimes with vanishing concircular curvature tensor have also been considered. The divergence of concircular curvature tensor is studied in detail and it is seen, among other results, that if the divergence of the concircular tensor is zero and the Ricci tensor is of Codazzi type then the resulting spacetime is of constant curvature. For a perfect fluid spacetime to possess divergence-free concircular curvature tensor, a necessary and sufficient condition has been obtained in terms of Friedmann-Robertson-Walker model.

show abstract

“…Now if we consider (ZRF) n manifold on which the Z tensor is a Codazzi one [17]; we have simply from Eq. (2.14)…”

Section: Definition 25mentioning

confidence: 99%

“…where A and B are non-null constants, ψ an arbitrary scalar function and a kl a symmetric (0.2) Codazzi tensor, [17] i.e. ∇ i a kl = ∇ k a il .…”

Section: Recurrent Z Forms On Riemannian and Kaehler Manifoldsmentioning

confidence: 99%

Recurrent Z Forms on Riemannian and Kaehler Manifolds

Mantica

Suh

2012

Int. J. Geom. Methods Mod. Phys.

View full text Add to dashboard Cite

In this paper, we introduce a new kind of Riemannian manifold that generalize the concept of weakly Z-symmetric and pseudo-Z-symmetric manifolds. First a Z form associated to the Z tensor is defined. Then the notion of Z recurrent form is introduced. We take into consideration Riemannian manifolds in which the Z form is recurrent. This kind of manifold is named (ZRF)n. The main result of the paper is that the closedness property of the associated covector is achieved also for rank(Z kl ) > 2. Thus the existence of a proper concircular vector in the conformally harmonic case and the form of the Ricci tensor are confirmed for(ZRF)n manifolds with rank(Z kl ) > 2. This includes and enlarges the corresponding results already proven for pseudo-Z-symmetric (PZS)n and weakly Z-symmetric manifolds (WZS)n in the case of non-singular Z tensor. In the last sections we study special conformally flat (ZRF)n and give a brief account of Z recurrent forms on Kaehler manifolds.

show abstract

Codazzi Tensor Fields, Curvature and Pontryagin Forms

Cited by 70 publications

References 12 publications

Curvature properties of Gödel metric

Curvature properties of Gödel metric

Concircular Curvature Tensor and Fluid Spacetimes

Recurrent Z Forms on Riemannian and Kaehler Manifolds

Contact Info

Product

Resources

About