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Czasopisma help

  1. 3 Colloquium Mathematicum

Autorzy help

  1. 3 Mantica C.

  2. 3 Molinari L.

Lata help

  1. 2 2012

  2. 1 2011

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Extended Derdziński-Shen theorem for curvature tensors

100%
Mantica C., Molinari L.
Colloquium Mathematicum
|
2012
|
tom 128
|
nr 1
1-6
EN
We extend a remarkable theorem of Derdziński and Shen, on the restrictions imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor. We show that the Codazzi equation can be replaced by a more general algebraic condition. The resulting extension applies both to the Riemann tensor and to generalized curvature tensors.
2
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Riemann compatible tensors

100%
Mantica C., Molinari L.
Colloquium Mathematicum
|
2012
|
tom 128
|
nr 2
197-210
EN
Derdziński and Shen's theorem on the restrictions on the Riemann tensor imposed by existence of a Codazzi tensor holds more generally when a Riemann compatible tensor exists. Several properties are shown to remain valid in this broader setting. Riemann compatibility is equivalent to the Bianchi identity for a new "Codazzi deviation tensor", with a geometric significance. The above general properties are studied, with their implications on Pontryagin forms. Examples are given of manifolds with Riemann compatible tensors, in particular those generated by geodesic mappings. Compatibility is extended to generalized curvature tensors, with an application to Weyl's tensor and general relativity.
3
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A second-order identity for the Riemann tensor and applications

100%
Mantica C., Molinari L.
Colloquium Mathematicum
|
2011
|
tom 122
|
nr 1
69-82
EN
A second-order differential identity for the Riemann tensor is obtained on a manifold with a symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors are derived from it. Applications to manifolds with recurrent or symmetric structures are discussed. The new structure of K-recurrency naturally emerges from an invariance property of an old identity due to Lovelock.
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