The Jordan normal form of Osserman algebraic curvature tensors

2001 ◽  
Vol 40 (1-4) ◽  
pp. 192-204 ◽  
Author(s):  
Peter Gilkey ◽  
Raina Ivanova
Keyword(s):  
Normal Form ◽  
Jordan Normal Form ◽  
Algebraic Curvature ◽  
Curvature Tensors

Conformai Curvature Tensors

2011 ◽  
Author(s):  
Charles Fefferman ◽  
C. Robin Graham
Keyword(s):  
Normal Form ◽  
Curvature Tensor ◽  
Riemannian Metric ◽  
Conformal Group ◽  
Conformal Change ◽  
Conformal Curvature ◽  
Covariant Derivatives ◽  
Curvature Tensors ◽  
Derivatives Of

This chapter studies conformal curvature tensors of a pseudo-Riemannian metric g. These are defined in terms of the covariant derivatives of the curvature tensor of an ambient metric in normal form relative to g. Their transformation laws under conformal change are given in terms of the action of a subgroup of the conformal group O(p + 1, q + 1) on tensors. It is assumed throughout this chapter that n ≥ 3.

Algebraic properties of a digraph and its line digraph

2003 ◽  
Vol 04 (04) ◽  
pp. 377-393 ◽  
Author(s):  
C. Balbuena ◽  
D. Ferrero ◽  
X. Marcote ◽  
I. Pelayo
Keyword(s):  
Normal Form ◽  
Characteristic Polynomials ◽  
Jordan Normal Form ◽  
Line Digraph ◽  
Algebraic Properties ◽  
Adjacency Matrices ◽  
Number Of Cycles

Let G be a digraph, LG its line digraph and A(G) and A(LG) their adjacency matrices. We present relations between the Jordan Normal Form of these two matrices. In addition, we study the spectra of those matrices and obtain a relationship between their characteristic polynomials that allows us to relate properties of G and LG, specifically the number of cycles of a given length.

scholarly journals A note on the structure of algebraic curvature tensors

2004 ◽  
Vol 382 ◽  
pp. 271-277 ◽  
Author(s):  
J.Carlos Dı́az-Ramos ◽  
Eduardo Garcı́a-Rı́o
Keyword(s):  
Algebraic Curvature ◽  
Curvature Tensors

scholarly journals On quasi-Clifford Osserman curvature tensors

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1241-1247
Author(s):  
Vladica Andrejic ◽  
Katarina Lukic
Keyword(s):  
Curvature Tensor ◽  
Sufficient Conditions ◽  
Duality Principle ◽  
Algebraic Curvature ◽  
Curvature Tensors

We consider pseudo-Riemannian generalizations of Osserman, Clifford, and the duality principle properties for algebraic curvature tensors and investigate relations between them. We introduce quasi- Clifford curvature tensors using a generalized Clifford family and show that they are Osserman. This allows us to discover an Osserman curvature tensor that does not satisfy the duality principle. We give some necessary and some sufficient conditions for the total duality principle.

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