Publication detail

# Examples of Homothety Curvature Homogeneous Spaces

VANŽUROVÁ, A.

Original Title

Examples of Homothety Curvature Homogeneous Spaces

English Title

Examples of Homothety Curvature Homogeneous Spaces

Type

conference paper

Language

en

Original Abstract

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.

English abstract

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.

Keywords

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

Released

14.06.2018

Location

University of Defence, Brno

ISBN

978-80-7582-065-5

Book

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

Pages from

134

Pages to

145

Pages count

12

Documents

BibTex

```
@inproceedings{BUT151953,
author="Alena {Vanžurová}",
title="Examples of Homothety Curvature Homogeneous Spaces",
annote="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.
",
booktitle="Mathematics, Information Technologies and Applied Sciences 2018, post-conference proceedings of extended versions of selected papers",
chapter="151953",
howpublished="electronic, physical medium",
year="2018",
month="june",
pages="134--145",
type="conference paper"
}
```