Riemannian Hilbert Manifolds

DOI10.1007/978-981-10-5556-0_22zbMath1390.58004arXiv1610.01527OpenAlexW2527960828MaRDI QIDQ4609947

Francesco Mercuri, Leonardo Biliotti

Publication date: 27 March 2018

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.01527

zbMATH Keywords

conjugate pointsJacobi fieldsRiemannian Hilbert manifoldHopf-Rinow manifold

Mathematics Subject Classification ID

Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20)

Cites Work

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• Geometry of diffeomorphism groups, complete integrability and geometric statistics
• Properly discontinuous actions on Hilbert manifolds
• The exponential map near conjugate points in 2D hydrodynamics
• The automorphism group of a Banach principal bundle with \{1\}-structure
• Geodesics in infinite dimensional Stiefel and Grassmann manifolds
• Infinite dimensional Riemannian symmetric spaces with fixed-sign curvature operator
• Locally symmetric homogeneous spaces
• The Hopf-Rinow theorem in infinite dimension
• The exponential map on the free loop space is Fredholm
• The exponential map of a weak Riemannian Hilbert manifold
• Properly discontinuous isometric actions on the unit sphere of infinite dimensional Hilbert spaces
• Homogeneity and bounded isometries in manifolds of negative curvature
• Approximation methods by regular functions
• On the singularities of the exponential map in infinite dimensional Riemannian manifolds
• Morse theory on Hilbert manifolds
• Curvatures of Sobolev metrics on diffeomorphism groups
• Fredholm properties of Riemannian exponential maps on diffeomorphism groups
• Banach Symmetric Spaces
• The Existence of Complete Riemannian Metrics
• Riemannian center of mass and mollifier smoothing
• The Hopf-Rinow Theorem is false in infinite Dimensions
• Exponential maps of Sobolev metrics on loop groups
• A note on tensor fields in Hilbert spaces
• Clifford Translations of Symmetric Spaces
• Conjugate points in $\mathcal {D}_{\mu }(T^2)$
• Locally Symmetric Homogeneous Finsler Spaces
• Hilbert Manifolds Without Epiconjugate Points
• Riemannian geometry

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