Displaying similar documents to “Remarks on algebraic concomitants of the Riemann-Christoffel curvature tensor in a three-dimensional space”

Extended Derdziński-Shen theorem for curvature tensors

Carlo Alberto Mantica, Luca Guido Molinari (2012)

Colloquium Mathematicae

Similarity:

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.

Riemann compatible tensors

Carlo Alberto Mantica, Luca Guido Molinari (2012)

Colloquium Mathematicae

Similarity:

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...

Surfaces with non-zero normal curvature tensor

Antonio Carlos Asperti, Dirk Ferus, Lucio Rodriguez (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Studiamo la topologia differenziale e la geometria delle superfici compatte con curvatura normale non-nulla in spazio della curvatura costante.