Riemannian Symmetric

Some articles on symmetric, riemannian, riemannian symmetric:

Riemannian Connection On A Surface - Example: The 2-sphere
... The Lie algebra of SO(3) consists of all skew-symmetric real 3 x 3 matrices ... to the 3-sphere and under this identification the standard Riemannian metric on the 3-sphere becomes the essentially unique biinvariant Riemannian. 3 and itself has an essentially unique biinvariant Riemannian metric ...
Classification of Riemannian Symmetric Spaces
... The algebraic description of Riemannian symmetric spaces enabled Élie Cartan to obtain a complete classification of them in 1926 ... For a given Riemannian symmetric space M let (G,K,σ,g) be the algebraic data associated to it ...
Classification of Riemannian Symmetric Spaces - Classification Scheme
... A simply connected Riemannian symmetric space is said to be irreducible if it is not the product of two or more Riemannian symmetric spaces ... It can then be shown that any simply connected Riemannian symmetric space is a Riemannian product of irreducible ones ... we may further restrict ourselves to classifying the irreducible, simply connected Riemannian symmetric spaces ...
Classification of Riemannian Symmetric Spaces - As Grassmannians
... modern classification (Huang Leung 2011) uniformly classifies the Riemannian symmetric spaces, both compact and non-compact, via a Freudenthal magic square construction ... The irreducible compact Riemannian symmetric spaces are, up to finite covers, either a compact simple Lie group, a Grassmannian, a Lagrangian Grassmannian, or a double Lagrangian ... construction produces the irreducible non-compact Riemannian symmetric spaces ...