Detail publikace

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

HINTERLEITNER, I. MIKEŠ, J. PEŠKA, P.

Originální název

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

Typ

článek v časopise ve Scopus, Jsc

Jazyk

angličtina

Originální abstrakt

We study special F-planar mappings between two n-dimensional (pseudo-) Riemannian manifolds. In 2003 Topalov introduced $PQ^{\varepsilon}$-projectivity of Riemannian metrics, $\varepsilon\neq 1,1+n$. 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.

Klíčová slova

$F^\varepsilon_2$-planar mapping; $PQ^\varepsilon$-projective equivalence; F-planar mapping; fundamental equation; (pseudo-) Riemannian manifold.

Autoři

HINTERLEITNER, I.; MIKEŠ, J.; PEŠKA, P.

Rok RIV

2014

Vydáno

19. 12. 2014

Nakladatel

Masaryk University

Místo

Brno, Czech Republic

ISSN

0044-8753

Periodikum

ARCHIVUM MATHEMATICUM

Ročník

50

Číslo

5

Stát

Česká republika

Strany od

33

Strany do

41

Strany počet

9

BibTex

@article{BUT110152,
  author="Irena {Hinterleitner} and Josef {Mikeš} and Patrik {Peška}",
  title="On $F^\varepsilon_2$-planar mappings of (pseudo-) Riemannian manifolds",
  journal="ARCHIVUM MATHEMATICUM",
  year="2014",
  volume="50",
  number="5",
  pages="33--41",
  doi="10.5817/AM2014-5-287",
  issn="0044-8753"
}