Detail publikace

Examples of Homothety Curvature Homogeneous Spaces

VANŽUROVÁ, A.

Originální název

Examples of Homothety Curvature Homogeneous Spaces

Typ

článek ve sborníku ve WoS nebo Scopus

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

VANŽUROVÁ, A.

Vydáno

14. 6. 2018

Místo

University of Defence, Brno

ISBN

978-80-7582-065-5

Kniha

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

Strany od

134

Strany do

145

Strany počet

12

BibTex

@inproceedings{BUT151953,
  author="Alena {Vanžurová}",
  title="Examples of Homothety Curvature Homogeneous Spaces",
  booktitle="Mathematics, Information Technologies and Applied Sciences 2018, post-conference proceedings of extended versions of  selected papers",
  year="2018",
  pages="134--145",
  address="University of Defence, Brno",
  isbn="978-80-7582-065-5"
}