Infinite dimensional Riemannian symmetric spaces with fixed-sign curvature operator
Differential Geometry
2021-02-03 v2
Abstract
We associate to any Riemannian symmetric space (of finite or infinite dimension) a L-algebra, under the assumption that the curvature operator has a fixed sign. L-algebras are Lie algebras with a pleasant Hilbert space structure. The L-algebra that we construct is a complete local isomorphism invariant and allows us to classify Riemannian symmetric spaces with fixed-sign curvature operator. The case of nonpositive curvature is emphasized.
Keywords
Cite
@article{arxiv.1204.6012,
title = {Infinite dimensional Riemannian symmetric spaces with fixed-sign curvature operator},
author = {Bruno Duchesne},
journal= {arXiv preprint arXiv:1204.6012},
year = {2021}
}
Comments
A para\^itre aux annales de l'institut Fourier