scholarly journals SPACELIKE JORDAN OSSERMAN ALGEBRAIC CURVATURE TENSORS IN THE HIGHER SIGNATURE SETTING

2002 ◽  
Author(s):  
PETER B. GILKEY ◽  
RAINA IVANOVA
Keyword(s):  
Algebraic Curvature ◽  
Curvature Tensors

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.

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

scholarly journals PSEUDO-RIEMANNIAN JACOBI–VIDEV MANIFOLDS

2007 ◽  
Vol 04 (05) ◽  
pp. 727-738 ◽  
Author(s):  
P. GILKEY ◽  
S. NIKČEVIĆ
Keyword(s):  
Riemannian Manifolds ◽  
Complex Structure ◽  
Almost Complex Structure ◽  
Ricci Operator ◽  
Almost Complex ◽  
Algebraic Curvature ◽  
Curvature Tensors

We exhibit several families of Jacobi–Videv pseudo-Riemannian manifolds which are not Einstein. We also exhibit Jacobi–Videv algebraic curvature tensors where the Ricci operator defines an almost complex structure.

PSEUDO-SYMMETRIC LORENTZIAN THREE-MANIFOLDS

2009 ◽  
Vol 06 (07) ◽  
pp. 1135-1150 ◽  
Author(s):  
G. CALVARUSO ◽  
B. DE LEO
Keyword(s):  
Three Dimensional ◽  
Ricci Operator ◽  
Algebraic Curvature ◽  
Segre Types ◽  
Curvature Tensors

We investigate pseudo-symmetric Lorentzian three-manifolds for the different possible Segre types of the Ricci operator. After determining all three-dimensional pseudo-symmetric Lorentzian algebraic curvature tensors, we classify pseudo-symmetric Lorentzian three-spaces which are either homogeneous, curvature homogeneous up to order 1 or curvature homogeneous, and we also provide some examples which are not curvature homogeneous.

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