Examples of Homothety Curvature Homogeneous Spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F18%3APU130193" target="_blank" >RIV/00216305:26110/18:PU130193 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Examples of Homothety Curvature Homogeneous Spaces
Original language description
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.
Czech name
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Czech description
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Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Mathematics, Information Technologies and Applied Sciences 2018, post-conference proceedings of extended versions of selected papers
ISBN
978-80-7582-065-5
ISSN
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e-ISSN
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Number of pages
12
Pages from-to
134-145
Publisher name
Neuveden
Place of publication
University of Defence, Brno
Event location
Brno
Event date
Jun 14, 2018
Type of event by nationality
EUR - Evropská akce
UT code for WoS article
000570646000015

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