A five-dimensional Riemannian manifold with an irreducible SO(3)-structure as a model of abstract statistical manifold

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F14%3A33146219" target="_blank" >RIV/61989592:15310/14:33146219 - isvavai.cz</a>

Výsledek na webu

<a href="http://download.springer.com/static/pdf/699/art%253A10.1007%252Fs10455-013-9390-0.pdf?auth66=1397737950_61bfbd153102ad3ececeb66b09182f05&ext=.pdf" target="_blank" >http://download.springer.com/static/pdf/699/art%253A10.1007%252Fs10455-013-9390-0.pdf?auth66=1397737950_61bfbd153102ad3ececeb66b09182f05&ext=.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10455-013-9390-0" target="_blank" >10.1007/s10455-013-9390-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A five-dimensional Riemannian manifold with an irreducible SO(3)-structure as a model of abstract statistical manifold

Popis výsledku v původním jazyce

In the present paper, we consider a five-dimensional Riemannian manifold with an irreducible SO(3)-structure as an example of an abstract statistical manifold. We prove that if a five-dimensional Riemannian manifold with an irreducible SO(3)-structure isa statistical manifold of constant curvature, then the metric of the Riemannian manifold is an Einstein metric. In addition, we show that a five-dimensional Euclidean sphere with an irreducible SO(3)-structure cannot be a conjugate symmetric statisticalmanifold. Finally, we show some results for a five-dimensional Riemannian manifold with a nearly integrable SO(3)-structure. For example, we prove that the structure tensor of a nearly integrable SO(3)-structure on a five-dimensional Riemannian manifoldis a harmonic symmetric tensor and it defines the first integral of third order of the equations of geodesics. Moreover, we consider some topological properties of five-dimensional compact and conformally flat Riemannian manifolds with i

Název v anglickém jazyce

A five-dimensional Riemannian manifold with an irreducible SO(3)-structure as a model of abstract statistical manifold

Popis výsledku anglicky

In the present paper, we consider a five-dimensional Riemannian manifold with an irreducible SO(3)-structure as an example of an abstract statistical manifold. We prove that if a five-dimensional Riemannian manifold with an irreducible SO(3)-structure isa statistical manifold of constant curvature, then the metric of the Riemannian manifold is an Einstein metric. In addition, we show that a five-dimensional Euclidean sphere with an irreducible SO(3)-structure cannot be a conjugate symmetric statisticalmanifold. Finally, we show some results for a five-dimensional Riemannian manifold with a nearly integrable SO(3)-structure. For example, we prove that the structure tensor of a nearly integrable SO(3)-structure on a five-dimensional Riemannian manifoldis a harmonic symmetric tensor and it defines the first integral of third order of the equations of geodesics. Moreover, we consider some topological properties of five-dimensional compact and conformally flat Riemannian manifolds with i

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

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

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 periodika

Annals of Global Analysis and Geometry

ISSN

0232-704X

e-ISSN

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Svazek periodika

45

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

18

Strana od-do

111-128

Kód UT WoS článku

000331704500002

EID výsledku v databázi Scopus

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