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Manifolds with a non-degenerate symmetric bilinear form in each tangent space varying differentiably but with constant index and signature.

2 votes
0 answers
77 views

Examples of curvature-adapted subgroups of semi-Riemannian groups

Let $G$ be a semi-Riemannian group, i.e., a Lie group equipped with a bi-invariant semi-Riemannian metric. I am looking for examples of Lie subgroups that are curvature adapted to $G$. First, allow me …
Matteo Raffaelli's user avatar
5 votes
1 answer
173 views

Proof of equivalence between Lie triple systems and totally geodesic submanifolds

In a Riemannian symmetric space $Q$, it is well known that the existence of a totally geodesic submanifold at a point $p \in Q$ is equivalent to the existence of a Lie triple system at $p$, i.e., a su …
Matteo Raffaelli's user avatar