  Recent developments in string theory suggest that there might exist extra
spatial dimensions, which are not small nor compact. The framework of a great
number of brane cosmological models is that in which the matter fields are
confined on a brane-world embedded in five dimensions (the bulk). Motivated by
this we review the main results on the algebraic classification of second order
symmetric tensors in 5-dimensional space-times. All possible Segre types for a
symmetric two-tensor are found, and a set of canonical forms for each Segre
type is obtained. A limiting diagram for the Segre types of these symmetric
tensors in 5-D is built. Two theorems which collect together some basic results
on the algebraic structure of second order symmetric tensors in 5-D are
presented. We also show how one can obtain, by induction, the classification
and the canonical forms of a symmetric two-tensor on n-dimensional (n > 5)
spaces from its classification in 5-D spaces, present the Segre types in n-D
and the corresponding canonical forms. This classification of symmetric
two-tensors in any n-D spaces and their canonical forms are important in the
context of n-dimensional brane-worlds context and also in the framework of 11-D
supergravity and 10-D superstrings.
