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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
A five-dimensional Riemannian manifold with an irreducible SO(3)-structure as a model of abstract statistical manifold
Original language description
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
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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