Transformations between Singer-Thorpe bases in 4-dimensional Einstein manifolds

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10319187" target="_blank" >RIV/00216208:11320/15:10319187 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/62690094:18470/15:50003621

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Transformations between Singer-Thorpe bases in 4-dimensional Einstein manifolds

Popis výsledku v původním jazyce

It is well known that, at each point of a 4-dimensional Einstein Riemannian manifold (M, g), the tangent space admits at least one so-called Singer-Thorpe basis with respect to the curvature tensor R at p. K. Sekigawa put the question "how many" Singer-Thorpe bases exist for a fixed curvature tensor R. Here we work only with algebraic structures (V, <,>, R), where <,> is a positive scalar product and R is an algebraic curvature tensor (in the sense of P. Gilkey) which satisfies the Einstein property. Wegive a partial answer to the Sekigawa problem and we state a reasonable conjecture for the general case. Moreover, we solve completely a modified problem: how many there are orthonormal bases which are Singer-Thorpe bases simultaneously for a natural 5-dimensional family of Einstein curvature tensors R. The answer is given by what we call "the universal Singer-Thorpe group" and we show that it is a finite group with 2304 elements.

Název v anglickém jazyce

Transformations between Singer-Thorpe bases in 4-dimensional Einstein manifolds

Popis výsledku anglicky

It is well known that, at each point of a 4-dimensional Einstein Riemannian manifold (M, g), the tangent space admits at least one so-called Singer-Thorpe basis with respect to the curvature tensor R at p. K. Sekigawa put the question "how many" Singer-Thorpe bases exist for a fixed curvature tensor R. Here we work only with algebraic structures (V, <,>, R), where <,> is a positive scalar product and R is an algebraic curvature tensor (in the sense of P. Gilkey) which satisfies the Einstein property. Wegive a partial answer to the Sekigawa problem and we state a reasonable conjecture for the general case. Moreover, we solve completely a modified problem: how many there are orthonormal bases which are Singer-Thorpe bases simultaneously for a natural 5-dimensional family of Einstein curvature tensors R. The answer is given by what we call "the universal Singer-Thorpe group" and we show that it is a finite group with 2304 elements.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP201%2F11%2F0356" target="_blank" >GAP201/11/0356: Riemannova, pseudo-Riemannova a afinní diferenciální geometrie</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Hokkaido Mathematical Journal

ISSN

0385-4035

e-ISSN

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Svazek periodika

44

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

JP - Japonsko

Počet stran výsledku

18

Strana od-do

441-458

Kód UT WoS článku

000367966200009

EID výsledku v databázi Scopus

2-s2.0-84950264981