First, we show that a warped product of line with Riemannian manifold (fiber) is weakly conformally flat and quasi Einstein if only the fiber in which case Bach flat. Finally, characterize classify contact manifolds satisfying (and doubly weakly) quasi-Einstein ( $$\eta $$ -Einstein) conditions.

an ideal i of a ring r is called right baer-ideal if there exists an idempotent e 2 r such that r(i) = er. we know that r is quasi-baer if every ideal of r is a right baer-ideal, r is n-generalized right quasi-baer if for each i e r the ideal in is right baer-ideal, and r is right principaly quasi-baer if every principal right ideal of r is a right baer-ideal. therefore the concept of baer idea...

in this paper, we introduce a method by which we can find a close connection between the set of prime $z$-ideals of $c(x)$ and the same of $c(y)$, for some special subset $y$ of $x$. for instance, if $y=coz(f)$ for some $fin c(x)$, then there exists a one-to-one correspondence between the set of prime $z$-ideals of $c(y)$ and the set of prime $z$-ideals of $c(x)$ not containing $f$. moreover, c...

Many authors have studied Ricci solitons and their analogs within the framework of (almost) contact geometry. In this article, we thoroughly study $$(m,\rho )$$ -quasi-Einstein structure on a metric manifold. First, prove that if K-contact or Sasakian manifold $$M^{2n+1}$$ admits closed structure, then it is an Einstein constant scalar curvature $$2n(2n+1)$$ , for particular case—a non-Sasak...

‎In this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional Euclidean spaces‎, ‎which are the Einstein and M"{o}bius gyrovector spaces‎. ‎We introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and explore its...

We numerically calculate Perelman’s entropy for a variety of canonical metrics on CP-bundles over products of Fano Kähler-Einstein manifolds. The metrics investigated are Einstein metrics, Kähler-Ricci solitons and quasi-Einstein metrics. The calculation of the entropy allows a rough picture of how the Ricci flow behaves on each of the manifolds in question.