Curvature homogeneous manifolds in dimension 4
| Autor: | Luigi Verdiani, Wolfgang Ziller |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Homogeneous manifolds 010102 general mathematics Dimension (graph theory) Curvature 01 natural sciences Action (physics) symbols.namesake 53C20 53C25 Differential Geometry (math.DG) Differential geometry Fourier analysis 0103 physical sciences Simply connected space FOS: Mathematics symbols 010307 mathematical physics Geometry and Topology Mathematics::Differential Geometry 0101 mathematics Invariant (mathematics) Mathematics |
| Popis: | We classify complete curvature homogeneous metrics on simply connected four dimensional manifolds which are invariant under a cohomogeneity one action. We show that they are either isometric to a symmetric space with one of its cohomogeneity one actions, or to a complete example by Tsukada on the normal bundle of the Veronese surface in CP^2. Along the way we show (in any dimension) that via an equivariant diffeomorphism the functions describing the metric can be partially diagonalized, a fact that may be useful for other problems as well Final version, to appear in Transformation Groups |
| Databáze: | OpenAIRE |
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