On dimensions of vector spaces of conformal Killing forms

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F14%3A33151204" target="_blank" >RIV/61989592:15310/14:33151204 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/978-3-642-55361-5_29" target="_blank" >http://dx.doi.org/10.1007/978-3-642-55361-5_29</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-642-55361-5_29" target="_blank" >10.1007/978-3-642-55361-5_29</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On dimensions of vector spaces of conformal Killing forms

Popis výsledku v původním jazyce

In this article there are found precise upper bounds of dimension of vector spaces of conformal Killing forms, closed and coclosed conformal Killing r-forms on an n-dimensional manifold. It is proved that, in the case of n-dimensional closed Riemannian manifold, the vector space of conformal Killing r-forms is an orthogonal sum of the subspace of Killing forms and of the subspace of exact conformal Killing r-forms. This is a generalization of related result of Tachibana and Kashiwada on pointwise decomposition of conformal Killing r-forms on a Riemannian manifold with constant curvature. It is shown that the following well known proposition may be derived as a consequence of our result: any closed Riemannian manifold having zero Betti number and admitting group of conformal mappings, which is non equal to the group of motions, is conformal equivalent to a hypersphere of Euclidean space.

Název v anglickém jazyce

On dimensions of vector spaces of conformal Killing forms

Popis výsledku anglicky

In this article there are found precise upper bounds of dimension of vector spaces of conformal Killing forms, closed and coclosed conformal Killing r-forms on an n-dimensional manifold. It is proved that, in the case of n-dimensional closed Riemannian manifold, the vector space of conformal Killing r-forms is an orthogonal sum of the subspace of Killing forms and of the subspace of exact conformal Killing r-forms. This is a generalization of related result of Tachibana and Kashiwada on pointwise decomposition of conformal Killing r-forms on a Riemannian manifold with constant curvature. It is shown that the following well known proposition may be derived as a consequence of our result: any closed Riemannian manifold having zero Betti number and admitting group of conformal mappings, which is non equal to the group of motions, is conformal equivalent to a hypersphere of Euclidean space.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

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

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název statě ve sborníku

Algebra, Geometry and Mathematical Physics

ISBN

978-3-642-55360-8

ISSN

—

e-ISSN

—

Počet stran výsledku

9

Strana od-do

495-507

Název nakladatele

Springer

Místo vydání

Heidelberg

Místo konání akce

Mulhouse, France

Datum konání akce

24. 10. 2011

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000347610400029