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

Irena Hinterleitner; Volodymyr A. Kiosak

Archivum Mathematicum (2008)

- Volume: 044, Issue: 5, page 385-390
- ISSN: 0044-8753

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topHinterleitner, Irena, and Kiosak, Volodymyr A.. "$\phi ({\rm Ric})$-vector fields in Riemannian spaces." Archivum Mathematicum 044.5 (2008): 385-390. <http://eudml.org/doc/250510>.

@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 -

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