In this paper we will investigate the global properties of complete Hilbert manifolds with upper and lower bounded sectional curvature. We shall prove the Focal Index lemma that will allow us to extend some classical results of finite dimensional Riemannian geometry as Rauch and Berger theorems and the Topogonov theorem in the class of manifolds in which the Hopf-Rinow theorem holds.
Some results on infinite dimensional riemannian geometry / Biliotti, L.. - In: ACTA SCIENTIARUM MATHEMATICARUM. - ISSN 0001-6969. - 72:1-2(2006), pp. 1-27.
Some results on infinite dimensional riemannian geometry
Biliotti L.
2006-01-01
Abstract
In this paper we will investigate the global properties of complete Hilbert manifolds with upper and lower bounded sectional curvature. We shall prove the Focal Index lemma that will allow us to extend some classical results of finite dimensional Riemannian geometry as Rauch and Berger theorems and the Topogonov theorem in the class of manifolds in which the Hopf-Rinow theorem holds.File in questo prodotto:
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