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On dimensions of vector spaces of conformal Killing forms

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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>

Alternative languages

  • Result language

    angličtina

  • Original language name

    On dimensions of vector spaces of conformal Killing forms

  • Original language description

    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.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/GAP201%2F11%2F0356" target="_blank" >GAP201/11/0356: Riemannian, pseudo-Riemannian and affine differential geometry</a><br>

  • Continuities

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

Others

  • Publication year

    2014

  • Confidentiality

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

Data specific for result type

  • Article name in the collection

    Algebra, Geometry and Mathematical Physics

  • ISBN

    978-3-642-55360-8

  • ISSN

  • e-ISSN

  • Number of pages

    9

  • Pages from-to

    495-507

  • Publisher name

    Springer

  • Place of publication

    Heidelberg

  • Event location

    Mulhouse, France

  • Event date

    Oct 24, 2011

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article

    000347610400029