φ ( Ric ) -vector fields in Riemannian spaces

Irena Hinterleitner; Volodymyr A. Kiosak

Archivum Mathematicum (2008)

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

Abstract

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In this paper we study vector fields in Riemannian spaces, which satisfy ∇ ϕ = μ , 𝐑𝐢𝐜 , μ = 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 ϕ ( Ric ) -vector fields cannot exist simultaneously. It was found that Riemannian spaces with ϕ ( Ric ) -vector fields of constant length have constant scalar curvature. The conditions for the existence of ϕ ( Ric ) -vector fields in symmetric spaces are given.

How to cite

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Hinterleitner, 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 -

References

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  6. Mikeš, J., Hinterleitner, I., Kiosak, V. A., On the theory of geodesic mappings of Einstein spaces and their generalizations, AIP Conf. Proc., 2006, pp. 428–435. (2006) 
  7. Mikeš, J., Rachůnek, L., On tensor fields semiconjugated with torse-forming vector fields, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 44 (2005), 151–160. (2005) Zbl1092.53016MR2218574
  8. Mikeš, J., Škodová, M., Concircular vector fields on compact spaces, Publ. de la RSME 11 (2007), 302–307. (2007) 
  9. Shandra, I. G., Concircular vector fields on semi-riemannian spaces, J. Math. Sci. 31 (2003), 53–68. (2003) MR2464554
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