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

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/00216305:26110/14:PU111002

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

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

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název periodika

Archivum Mathematicum

ISSN

0044-8753

e-ISSN

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Svazek periodika

50

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

9

Strana od-do

33-41

Kód UT WoS článku

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EID výsledku v databázi Scopus

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