Riemannian Symmetric

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 ... To classify possibly isometry classes of M, first note that the universal cover of a Riemannian symmetric space is again Riemannian symmetric, and the covering ...

Classification of Riemannian Symmetric Spaces - As Grassmannians
... 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 Grassmannian of ... produces the irreducible non-compact Riemannian symmetric spaces ...

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 ... diffeomorphic to the 3-sphere and under this identification the standard Riemannian metric on the 3-sphere becomes the essentially unique biinvariant Riemannian metric on SU(2) ... the real projective space of dimension 3 and itself has an essentially unique biinvariant Riemannian metric ...

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 ... restrict ourselves to classifying the irreducible, simply connected Riemannian symmetric spaces ...