Almost Osserman structures on natural Riemann extensions

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Almost Osserman structures on natural Riemann extensions
Original language description
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
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
<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)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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