Application of Hilbert’s Projective Metric on Symmetric Cones

The Projective Quarter Symmetric Metric Connections and Their Curvature Tensors

Spherical Functions on Symmetric Cones

In this note, we obtain a recursive formula for the spherical functions associated with the symmetric cone of a formally real Jordan algebra. We use this formula as an inspiration for a similar recursive formula involving the Jack polynomials.

Pseudo Ricci symmetric real hypersurfaces of a complex projective space

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.

On Weakly Projective Symmetric Manifolds

The object of the present paper is to study weakly projective symmetric manifolds and its decomposability with several non-trivial examples. Among others it is shown that in a decomposable weakly projective symmetric manifold both the decompositions are weakly Ricci symmetric.

Projective φ-symmetric K-contact manifold admitting quarter-symmetric metric connection

We obtain curvature tensor R̃(X, Y )Z w.r.t quarter-symmetric metric connection in terms of curvature tensor R(X,Y )Z relative to the Levi-civita connection in a K-contact manifold. Further, locally φ-symmetric, φ-symmetric and locally projective φ-symmetric K-contact manifolds with respect to the quarter-symmetric metric connection are studied and some results are obtained. The results are assi...