We show that, up to biholomorphism, there is at most one complete T n $T^n$ -invariant shrinking gradient Kähler–Ricci soliton on a non-compact toric manifold M. also establish uniqueness without assuming -invariance if the Ricci curvature bounded and vector field lies in Lie algebra t $\mathfrak {t}$ of . As an application, we isometry, unique with scalar C P 1 × $\mathbb {C}\mathbb {P}^{1} \t...

Abstract We will show that if a gradient shrinking Ricci soliton has an approximate symmetry on one scale, this propagates to larger scales. This is example of the shrinker principle which roughly states information radiates outwards for solitons.

In this paper, we study conformal submersions from Ricci solitons to Riemannian manifolds with non-trivial examples. First, some properties of the O’Neill tensor A in case submersion. We also find a necessary and sufficient condition for submersion be totally geodesic calculate total manifold such map different assumptions. Further, consider $$F:M \rightarrow N$$ soliton obtain conditions fiber...

We investigate the pinching problem for shrinking compact Ricci solitons. Firstly, we show that every $n$-dimensional $(n\ge 4)$ soliton $(M^n,g)$ is isometric to a finite quotient of $\mathbb S^n$ under an $L^{n/2}$-pinching condi

We obtain some properties of a hyperbolic Ricci soliton with certain types potential vector fields, and we point out conditions when it reduces to trivial soliton. also study those submanifolds whose fields are the tangential components concurrent field on ambient manifold, in particular, show that totally umbilical is an Einstein manifold. prove if hypersurface Riemannian manifold constant cur...