We give a sharp upper diameter bound for compact shrinking Ricci soliton in terms of its scalar curvature integral and the Perelman’s entropy functional. The cases could occur at round spheres. proof mainly relies on logarithmic Sobolev inequality gradient solitons Vitali-type covering argument.

Abstract In a recent paper, Brendle showed the uniqueness of Bryant soliton among 3-dimensional κ-solutions. this we present an alternative proof for fact and show that compact κ-solutions are rotationally symmetric. Our arose from independent work relating to our Strong Stability Theorem singular Ricci flows.

In this paper, first we define Clairaut Riemannian map between manifolds by using a geodesic curve on the base space and find necessary sufficient conditions for to be with nontrivial example. We also obtain condition harmonic. Thereafter, study from manifold Ricci soliton scalar curvatures of $rangeF_\ast$ $(rangeF_\ast)^\bot$ soliton. Further, leaves almost Einstein. vector field $\dot{\beta}...

In this article, we derived an equality for CR-warped product in a complex space form which forms the relationship between gradient and Laplacian of warping function second fundamental form. We necessary conditions submanifolds Ka¨hler manifold to be Einstein impact Ricci soliton. Some classification by using Euler–Lagrange equation, Dirichlet energy Hamiltonian is given. also derive some chara...

In this paper, we study Clairaut Riemannian maps whose total manifolds admit a Ricci soliton and give nontrivial example of such maps. First, calculate tensors scalar curvature Then obtain necessary conditions for the fibers to be Einstein almost solitons. We also condition vector field [Formula: see text] conformal, where is geodesic curve on manifold map. Further, show that if with potential ...

Ricci-like solitons with arbitrary potential are introduced and studied on Sasaki-like almost contact B-metric manifolds. A manifold of this type can be considered as an complex Riemannian which cone is a holomorphic manifold. The soliton under study characterized proved that its Ricci tensor equal to the vertical component both B-metrics multiplied by constant. Thus, scalar curvatures respect ...

The present paper is to deliberate the class of $3$-dimensional trans-Sasakian manifolds which admits $\eta$-Einstein solitons. We have studied solitons on where Ricci tensors are Codazzi type and cyclic parallel. also discussed some curvature conditions admitting vector field torse-forming. shown an example manifold with respect soliton verify our results.

Abstract In the present paper, we consider non-reductive four-dimensional homogeneous spaces and classify generalized Ricci solitons on these spaces. We show that any space admits least in a soliton. Also, will prove have non-trivial Killing vector fields exclusive of types A1, A4 B2 are Einstein manifold admit solitons.