Conformally flat metric is said to be Ricci superosculating with at the point if , , , where is the Ricci tensor. In this paper the following theorem is proved: If is a smooth curve of the Riemannian manifold (without self-crossing(, then there is a neighbourhood of and a conformally flat metric which is the Ricci superosculating with along the curve .
Our aim is to apply suitable generalized maximum principles in order to obtain characterization results concerning complete linear Weingarten hypersurfaces immersed in a locally symmetric Riemannian manifold, whose sectional curvature is supposed to obey standard constraints. In this setting, we establish sufficient conditions to guarantee that such a hypersurface must be either totally umbilical or an isoparametric hypersurface with two distinct principal curvatures one of which is simple.
The object of the present paper is to study decomposable almost pseudo conharmonically symmetric manifolds.