Examples of Homothety Curvature Homogeneous Spaces

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Examples of Homothety Curvature Homogeneous Spaces

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Examples of Homothety Curvature Homogeneous Spaces

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

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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Počet stran výsledku

12

Strana od-do

134-145

Název nakladatele

Neuveden

Místo vydání

University of Defence, Brno

Místo konání akce

Brno

Datum konání akce

14. 6. 2018

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000570646000015