Almost Osserman structures on natural Riemann extensions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10173713" target="_blank" >RIV/00216208:11320/13:10173713 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.difgeo.2012.10.007" target="_blank" >http://dx.doi.org/10.1016/j.difgeo.2012.10.007</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.difgeo.2012.10.007" target="_blank" >10.1016/j.difgeo.2012.10.007</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Almost Osserman structures on natural Riemann extensions

Popis výsledku v původním jazyce

We study natural Einstein Riemann extensions of torsion-free affine manifolds (M, del). Such a Riemann extension of n-dimensional (M, del) is always a pseudo-Riemannian manifold of signature (n, n). It is well known that, if the base manifold (M, del) isa torsion-free affine two-manifold with skew-symmetric Ricci tensor, or a flat affine space, we obtain a (globally) Osserman structure on the cotangent bundle T*M over (M, del). If the new base manifold is an arbitrary direct product of the simple affine manifolds described above, we found that the resulting structures on T*M are not Osserman but only "almost Osserman", in the sense that the Jacobi operator has to be restricted from the whole set of space-like unit vectors (or time-like unit vectors, respectively) to a complement of a subset of measure zero. We also find that the characteristic polynomial of the (restricted) Jacobi operator in the cotangent bundle depends only on the full dimension n of the base manifold, and it is the

Název v anglickém jazyce

Almost Osserman structures on natural Riemann extensions

Popis výsledku anglicky

We study natural Einstein Riemann extensions of torsion-free affine manifolds (M, del). Such a Riemann extension of n-dimensional (M, del) is always a pseudo-Riemannian manifold of signature (n, n). It is well known that, if the base manifold (M, del) isa torsion-free affine two-manifold with skew-symmetric Ricci tensor, or a flat affine space, we obtain a (globally) Osserman structure on the cotangent bundle T*M over (M, del). If the new base manifold is an arbitrary direct product of the simple affine manifolds described above, we found that the resulting structures on T*M are not Osserman but only "almost Osserman", in the sense that the Jacobi operator has to be restricted from the whole set of space-like unit vectors (or time-like unit vectors, respectively) to a complement of a subset of measure zero. We also find that the characteristic polynomial of the (restricted) Jacobi operator in the cotangent bundle depends only on the full dimension n of the base manifold, and it is the

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

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

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

Differential Geometry and its Application

ISSN

0926-2245

e-ISSN

—

Svazek periodika

31

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

10

Strana od-do

140-149

Kód UT WoS článku

000315069000012

EID výsledku v databázi Scopus

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