Short survey on the existence of slices for the space of Riemannian metrics

DOI10.1090/conm/775/15589zbMath1496.58002arXiv1904.07031OpenAlexW3215032231MaRDI QIDQ5085337

Diego Corro, Jan-Bernhard Kordaß

Publication date: 27 June 2022

Published in: Mexican Mathematicians in the World (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.07031

zbMATH Keywords

Riemannian metricsLie group actionsdiffeomorphism groupstubular neighborhoods

Mathematics Subject Classification ID

Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Global Riemannian geometry, including pinching (53C20) (G)-structures (53C10) Manifolds of metrics (especially Riemannian) (58D17)

Related Items

Moduli space of non-negative sectional or positive Ricci curvature metrics on sphere bundles over spheres and their quotients, Non-trivial smooth families of \(K3\) surfaces, The covariance metric in the Blaschke locus

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Moduli spaces of Riemannian metrics
• The Ricci flow in Riemannian geometry. A complete proof of the differentiable 1/4-pinching sphere theorem
• On the existence of slices for actions of non-compact Lie groups
• Proper smooth \(G\)-manifolds have complete \(G\)-invariant Riemannian metrics
• The basic geometry of the manifold of Riemannian metrics and of its quotient by the diffeomorphism group
• Teichmüller space of negatively curved metrics on complex hyperbolic manifolds is not contractible
• Semicontinuity of compact group actions on compact differentiable manifolds
• Transformation groups in differential geometry.
• Slice theorem and orbit type stratification in infinite dimensions
• Some decompositions of the space of symmetric tensors on a Riemannian manifolds
• The Geometry of Infinite-Dimensional Groups
• The inverse function theorem of Nash and Moser
• THE RIEMANNIAN MANIFOLD OF ALL RIEMANNIAN METRICS
• A panoramic glimpse of manifolds with sectional curvature bounded from below
• Lie Groups and Geometric Aspects of Isometric Actions
• The Completion of the Manifold of Riemannian Metrics with Respect to its $L^2$ Metric