English

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