On almost pseudo concircular Ricci symmetric manifolds. (English) Zbl 1370.53017

Hui, Shyamal Kumar; Zengin, Füsun Özen

Bol. Asoc. Mat. Venez. 19, No. 1, 57-70 (2012).

Summary: The object of the present paper is to study almost pseudo concircular Ricci symmetric manifolds and its decomposibility. Among others it is shown that in a decomposable almost pseudo concircular Ricci symmetric manifold one of the decompositions is Einstein and the other decomposition is concircular Ricci symmetric. The totally umbilical hypersurfaces of almost pseudo concircular Ricci symmetric manifolds are also studied.

MSC:

53B30	Local differential geometry of Lorentz metrics, indefinite metrics
53B50	Applications of local differential geometry to the sciences
53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25	Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords:

pseudo Ricci symmetric manifold; almost pseudo Ricci symmetric manifold; 5concircular Ricci tensor; almost pseudo concircular Ricci symmetric manifold; scalar curvature; \(5W_2\)-curvature tensor; decomposable Riemannian manifold; totally umbilical hypersurfaces; 5totally geodesic; mean curvature