The object of the upcoming article is to characterize paracontact metric manifolds conceding $m$-quasi Einstein metric. First we establish that if $g$ in a $K$-paracontact manifold metric, then constant scalar curvature. Furthermore, classify $(k,\mu)$-paracontact whose Finally, construct non-trivial example such manifold.

The structure of the Wadge degrees on zero-dimensional spaces is very simple (almost well-ordered), but for many other natural non-zerodimensional spaces (including the space of reals) this structure is much more complicated. We consider weaker notions of reducibility, including the so-called ∆ 0 α-reductions, and try to find for various natural topological spaces X the least ordinal αX such th...

In this note, we prove that there is a canonical continuous Hermitian metric on the CM line bundle over the proper moduli space M of smoothable Kähler-Einstein Fano varieties. The curvature of this metric is the Weil-Petersson current, which exists as a positive (1,1)-current on M and extends the canonical Weil-Petersson current on the moduli space parametrizing smooth Kähler-Einstein Fano mani...

The profile of a relational structure R is the function φR which counts for every integer n the number φR(n), possibly infinite, of substructures of R induced on the n-element subsets, isomorphic substructures being identified. If φR takes only finite values, this is the Hilbert function of a graded algebra associated with R, the age algebra KA(R), introduced by P. J. Cameron. In this paper we ...

A Stiefel manifold VkR n is the set of orthonormal k-frames inR, and it is diffeomorphic to the homogeneous space SO(n)/SO(n−k). We study SO(n)-invariant Einstein metrics on this space. We determine when the standard metric on SO(n)/SO(n−k) is Einstein, and we give an explicit solution to the Einstein equation for the space V2R.