On pseudo semi-projective symmetric manifolds
In this paper we introduce a new tensor named semi-projec\-tive curvature tensor which generalizes the projective curvature tensor. First we deduce some basic geometric properties of semi-projective curvature tensor. Then we study pseudo semi-projective symmetric manifolds \linebreak $(PSPS)_{n}$ wh...
Gespeichert in:
Veröffentlicht in: | Journal of the Korean Mathematical Society 2018, 55(2), , pp.391-413 |
---|---|
Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | In this paper we introduce a new tensor named semi-projec\-tive curvature tensor which generalizes the projective curvature tensor. First we deduce some basic geometric properties of semi-projective curvature tensor. Then we study pseudo semi-projective symmetric manifolds \linebreak $(PSPS)_{n}$ which recover some known results of Chaki \cite{mcc3}. We provide several interesting results. Among others we prove that in a $(PSPS)_{n}$ if the associated vector field $\rho$ is a unit parallel vector field, then either the manifold reduces to a pseudosymmetric manifold or pseudo projective symmetric manifold. Moreover we deal with semi-projectively flat perfect fluid and dust fluid spacetimes respectively. As a consequence we obtain some important theorems. Next we consider the decomposability of $(PSPS)_{n}$. Finally, we construct a non-trivial Lorentzian metric of $(PSPS)_4$. KCI Citation Count: 0 |
---|---|
ISSN: | 0304-9914 2234-3008 |
DOI: | 10.4134/JKMS.j170252 |