scholarly journals Segre types of symmetric two-tensors inn-dimensional spacetimes

1995 ◽  
Vol 27 (9) ◽  
pp. 989-999 ◽  
Author(s):  
J. Santos ◽  
M. J. RebouÇas ◽  
A. F. F. Teixeira
Keyword(s):  
Segre Types

scholarly journals Limits of space–times in five dimensions and their relation to the Segre types

1997 ◽  
Vol 38 (8) ◽  
pp. 4228-4236 ◽  
Author(s):  
F. M. Paiva ◽  
M. J. Rebouças ◽  
A. F. F. Teixeira
Keyword(s):  
Five Dimensions ◽  
Segre Types

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.

scholarly journals Scalar polynomial curvature invariants in the context of the Cartan–Karlhede algorithm

2019 ◽  
Vol 16 (02) ◽  
pp. 1950027
Author(s):  
D. A. Brooks ◽  
D. D. McNutt ◽  
J. P. Simard ◽  
N. K. Musoke
Keyword(s):  
Ricci Tensor ◽  
Three Dimensional ◽  
Minimal Set ◽  
Curvature Invariants ◽  
Dimensional Gravity ◽  
Cartan Invariants ◽  
Segre Types

We employ the Cartan–Karlhede algorithm in order to completely characterize the class of Gödel-like spacetimes for three-dimensional gravity. By examining the permitted Segre types (or P-types) of the Ricci tensor, we present the results of the Cartan–Karlhede algorithm for each subclass in terms of the algebraically independent Cartan invariants at each order. Using this smaller subset of Cartan invariants, we express the scalar polynomial curvature invariants for the Gödel-like spacetimes in terms of this subset of Cartan invariants and generate a minimal set of scalar polynomial curvature invariants that uniquely characterize metrics in the class of Gödel-like spacetimes and identify the subclasses in terms of the P-types of the Ricci tensor.

scholarly journals A NOTE ON SEGRE TYPES OF SECOND-ORDER SYMMETRIC TENSORS IN 5-D BRANE-WORLD COSMOLOGY

2003 ◽  
Vol 18 (39) ◽  
pp. 2807-2815 ◽  
Author(s):  
M. J. REBOUÇAS ◽  
J. SANTOS
Keyword(s):  
Second Order ◽  
Brane World ◽  
Canonical Forms ◽  
Symmetric Tensors ◽  
Five Dimensions ◽  
Spatial Dimensions ◽  
Recent Developments ◽  
Segre Types ◽  
Matter Fields

Recent developments in string theory suggest that there might exist extra spatial dimensions, which are not small nor compact. The framework of most brane cosmological models is that the matter fields are confined on a brane-world embedded in five dimensions (the bulk). Motivated by this we re-examine the classification of the second-order symmetric tensors in 5-D, and prove two theorems which collect together some basic results on the algebraic structure of these tensors in five-dimensional spacetimes. We also briefly indicate how one can obtain, by induction, the classification of symmetric two-tensors (and the corresponding canonical forms) on n-dimensional (n>4) spaces from the classification on four-dimensional spaces. This is important in the context of 11-D supergravity and 10-D superstrings.

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