On $F^varepsilon_2$-planar mappings of (pseudo-) Riemannian manifolds

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F14%3A33157876" target="_blank" >RIV/61989592:15310/14:33157876 - isvavai.cz</a>
Alternative codes found
RIV/00216305:26110/14:PU111002
Result on the web
<a href="http://dml.cz/bitstream/handle/10338.dmlcz/144071/ArchMathRetro_050-2014-5_5.pdf" target="_blank" >http://dml.cz/bitstream/handle/10338.dmlcz/144071/ArchMathRetro_050-2014-5_5.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.5817/AM2014-5-287" target="_blank" >10.5817/AM2014-5-287</a>

Result language
angličtina
Original language name
On $F^varepsilon_2$-planar mappings of (pseudo-) Riemannian manifolds
Original language description
We study special F-planar mappings between two n-dimensional (pseudo-) Riemannian manifolds. In 2003 Topalov introduced $PQ^{varepsilon}$-projectivity of Riemannian metrics, $varepsilonneq 1,1+n$. Later these mappings were studied by Matveev and Rosemann. They found that for $varepsilon=0$ they are projective. We show that $PQ^{varepsilon}$-projective equivalence corresponds to a special case of F-planar mapping studied by Mikeš and Sinyukov (1983) and ${F_2}$-planar mappings (Mikeš, 1994), with F=Q. Moreover, the tensor P is derived from the tensor Q and the non-zero number $varepsilon$. For this reason we suggest to rename $PQ^{varepsilon}$ as ${F_2^{varepsilon}}$. We use earlier results derived for F- and $F_2$-planar mappings and find new results. For these mappings we find the fundamental partial differential equations in closed linear Cauchy type form and we obtain new results for initial conditions.
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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Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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