Curvature homogeneous manifolds in dimension 4

Luigi Verdiani; Wolfgang Ziller

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arXiv · 2006.11294

Curvature homogeneous manifolds in dimension 4

Luigi Verdiani·Wolfgang Ziller

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Abstract

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

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Luigi Verdiani, Wolfgang Ziller. 2020-06-19. Curvature homogeneous manifolds in dimension 4. https://arxiv.org/abs/2006.11294

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