$\phi \left(\mathrm{Ric}\right)$-vector fields in Riemannian spaces

@article{Hinterleitner2008,
abstract = {In this paper we study vector fields in Riemannian spaces, which satisfy $\nabla \varphi =\mu $, $\{\textbf \{Ric\}\}$, $\mu =\mbox\{const.\}$ We investigate the properties of these fields and the conditions of their coexistence with concircular vector fields. It is shown that in Riemannian spaces, noncollinear concircular and $\varphi (\mbox\{\textbf \{Ric\}\})$-vector fields cannot exist simultaneously. It was found that Riemannian spaces with $\varphi (\mbox\{\textbf \{Ric\}\})$-vector fields of constant length have constant scalar curvature. The conditions for the existence of $\varphi (\mbox\{\textbf \{Ric\}\})$-vector fields in symmetric spaces are given.},
author = {Hinterleitner, Irena, Kiosak, Volodymyr A.},
journal = {Archivum Mathematicum},
keywords = {special vector field; pseudo-Riemannian spaces; Riemannian spaces; symmetric spaces; Kasner metric; special vector field; pseudo-Riemannian space; Riemannian space; symmetric space; Kasner metric},
language = {eng},
number = {5},
pages = {385-390},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {$\phi (\{\rm Ric\})$-vector fields in Riemannian spaces},
url = {http://eudml.org/doc/250510},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Hinterleitner, Irena
AU - Kiosak, Volodymyr A.
TI - $\phi ({\rm Ric})$-vector fields in Riemannian spaces
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 5
SP - 385
EP - 390
AB - In this paper we study vector fields in Riemannian spaces, which satisfy $\nabla \varphi =\mu $, ${\textbf {Ric}}$, $\mu =\mbox{const.}$ We investigate the properties of these fields and the conditions of their coexistence with concircular vector fields. It is shown that in Riemannian spaces, noncollinear concircular and $\varphi (\mbox{\textbf {Ric}})$-vector fields cannot exist simultaneously. It was found that Riemannian spaces with $\varphi (\mbox{\textbf {Ric}})$-vector fields of constant length have constant scalar curvature. The conditions for the existence of $\varphi (\mbox{\textbf {Ric}})$-vector fields in symmetric spaces are given.
LA - eng
KW - special vector field; pseudo-Riemannian spaces; Riemannian spaces; symmetric spaces; Kasner metric; special vector field; pseudo-Riemannian space; Riemannian space; symmetric space; Kasner metric
UR - http://eudml.org/doc/250510
ER -