Examples of Homothety Curvature Homogeneous Spaces

conference paper

English

First we distinguish between curvature homogeneity and homothety curvature homogeneity. Curvature homogeneous manifolds are Riemannian spaces whose curvature tensor is, in some sense, ``the same" in all points, while for homothety curvature homogeneous spaces, cuvatures (and their covariant derivatives) in two points are related in a more general way. Trivial examples of curvature homogeneous spaces are homogeneous spaces and connected locally homogeneous manifolds. First non-trivial examples were discovered by K. Sekigawa and for a long time, only a few classes of such examples which are not locally homogeneous have been known. We study here an interesting class of metrics, given in arbitrary dimension, which are not locally homogeneous, and which generalize a 3-dimensional example originally given by K. Sekigawa. We also examine examples of ''Sekigawa type'' from the view-point of homothety curvature homogeneity.

Riemannian manifold; curvature tensor; curvature homogeneous manifold; locally homogeneous space

VANŽUROVÁ, A.

14. 6. 2018

University of Defence, Brno

978-80-7582-065-5

Mathematics, Information Technologies and Applied Sciences 2018, post-conference proceedings of extended versions of selected papers

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