Homothety Curvature Homogeneity and Homothety Homogeneity

E. Garcia-Rio; P. Gilkey; S. Nikcevic

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arXiv · 1403.6620

Homothety Curvature Homogeneity and Homothety Homogeneity

E. Garcia-Rio·P. Gilkey·S. Nikcevic

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Abstract

We examine the difference between several notions of curvature homogeneity and show that the notions introduced by Kowalski and Vanzurova are genuine generalizations of the ordinary notion of k-curvature homogeneity. The homothety group plays an essential role in the analysis. We give a complete classification of homothety homogeneous manifolds which are not homogeneous and which are not VSI and show that such manifolds are cohomogeneity one. We also give a complete description of the local geometry if the homothety character defines a split extension.

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BibTeX RIS

E. Garcia-Rio, P. Gilkey, S. Nikcevic. 2014-03-26. Homothety Curvature Homogeneity and Homothety Homogeneity. https://arxiv.org/abs/1403.6620

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