Walker manifolds of signature (2, 2) have been used by many authors to provide examples of Osserman and of conformal Osserman manifolds of signature (2, 2). We study questions of geodesic completeness and Ricci blowup in this context.

In this paper, we construct semisymmetric graphs in which no two vertices have exactly the same neighbors. We show how to do this by /rst considering bi-transitive graphs, and then we show how to choose two such graphs so that their product is regular. We display a family of bi-transitive graphs DN (a; b) which can be used for this purpose and we show that their products are semisymmetric by ap...

pseudo ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo ricci symmetric real hypersurfaces of the complex projective space cpn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.

A Riemannian manifold is called harmonic if its volume density function expressed in polar coordinates centered at any point of the manifold is radial. Flat and rank-one symmetric spaces are harmonic. The converse (the Lichnerowicz Conjecture) is true for manifolds of nonnegative scalar curvature and for some other classes of manifolds, but is not true in general: there exists a family of homog...

The object of the present paper is to study three-dimensional Lorentzian -Sasakian manifolds which are Ricci-semisymmetry, locally symmetric and have -parallel Ricci tensor. An example of a three-dimensional Lorentzian -Sasakian manifold is given which verifies all the Theorems.