$\phi({\rm Ric})$-vector fields in Riemannian spaces
Hinterleitner, Irena ; Kiosak, Volodymyr A.
Archivum Mathematicum, Tome 044 (2008), p. 385-390 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2008-01-01
Classification:  53B05,  53B30 
@article{127124,
     author = {Irena Hinterleitner and Volodymyr A. Kiosak},
     title = {$\phi({\rm Ric})$-vector fields in Riemannian spaces},
     journal = {Archivum Mathematicum},
     volume = {044},
     year = {2008},
     pages = {385-390},
     zbl = {1212.53018},
     mrnumber = {2501574},
     language = {en},
     url = {http://dml.mathdoc.fr/item/127124}
}

Hinterleitner, Irena; Kiosak, Volodymyr A. $\phi({\rm Ric})$-vector fields in Riemannian spaces. Archivum Mathematicum, Tome 044 (2008) pp. 385-390. http://gdmltest.u-ga.fr/item/127124/

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