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Article

De, Uday Chand ; Pal, Prajjwal
On Almost Pseudo-Z-symmetric Manifolds. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 53 (2014), issue 1, pp. 25-43
MSC: 53C25 | MR 3331069 | Zbl 1312.53065
Keywords:
pseudo symmetric manifolds; pseudo Ricci symmetric manifolds; almost pseudo Ricci symmetric manifolds; almost pseudo-Z-symmetric manifolds; conformally flat almost pseudo-Z-symmetric manifolds
Summary:
The object of the present paper is to study almost pseudo-Z-symmetric manifolds. Some geometric properties have been studied. Next we consider conformally flat almost pseudo-Z-symmetric manifolds. We obtain a sufficient condition for an almost pseudo-Z-symmetric manifold to be a quasi Einstein manifold. Also we prove that a totally umbilical hypersurface of a conformally flat $A(PZS)_{n}$ ($n>3$) is a manifold of quasi constant curvature. Finally, we give an example to verify the result already obtained in Section 5.
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