Related papers: Non-K\"ahler Expanding Ricci Solitons

For all complex dimensions n>=2, we construct complete Kaehler manifolds of bounded curvature and non-negative Ricci curvature whose Kaehler--Ricci evolutions immediately acquire Ricci curvature of mixed sign.

Some observations about the local and global generality of gradient Kahler Ricci solitons are made, including the existence of a canonically associated holomorphic volume form and vector field, the local generality of solutions with a…

Applying a well known result for attracting fixed points of biholomorphisms \cite{RR, V}, we observe that one immediately obtains the following result: if $(M^n,g)$ is a complete non-compact gradient K\"ahler-Ricci soliton which is either…

We construct metrics of positive Ricci curvature on some vector bundles over tori (or more generally, over nilmanifolds). This gives rise to the first examples of manifolds with positive Ricci curvature which are homotopy equivalent but not…

In this paper, we consider $n$-dimensional compact K$\ddot{a}$hler manifold with semi-ample canonical line bundle under the long time solution of K$\ddot{a}$hler Ricci Flow. In particular, if the Kodaira dimension is one, Ricci curvature…

We study the properties of Ricci curvature of ${\mathfrak{g}}$-manifolds with particular attention paid to higher dimensional abelian Lie algebra case. The relations between Ricci curvature of the manifold and the Ricci curvature of the…

In this paper, we prove that any complete shrinking gradient K\"ahler-Ricci solitons with positive orthogonal bisectional curvature must be compact. We also obtain a classification of the complete shrinking gradient K\"ahler-Ricci solitons…

In this paper we prove new classification results for nonnegatively curved gradient expanding and steady Ricci solitons in dimension three and above, under suitable integral assumptions on the scalar curvature of the underlying Riemannian…

In this note, we show that any $n$-dimensional $\kappa$-noncollapsed steady K\"ahler-Ricci soliton with nonnegative bisectional curvature must be flat. The result is an improvement to our former work in \cite{DZ2}.

In this paper, we prove that expanding gradient Ricci solitons with (positively) pinched Ricci curvature are trivial ones. Namely, they are either compact or flat.

We prove compactification theorems for some complete K\"ahler manifolds with nonnegative Ricci curvature. Among other things, we prove that a complete noncompact K\"ahler Ricci flat manifold with maximal volume growth and quadratic…

Considering pseudo-Riemannian $g$-natural metrics on tangent bundles, we prove that the condition of being Ricci soliton is hereditary in the sense that a Ricci soliton structure on the tangent bundle gives rise to a Ricci soliton structure…

We construct examples of Bach-flat gradient Ricci solitons which are neither half conformally flat nor conformally Einstein.

This paper studies cohomogeneity one Ricci solitons. If the isotropy representation of the principal orbit $G/K$ consists of two inequivalent $Ad_K$-invariant irreducible summands, the existence of parameter families of non-homothetic…

We derive a sharp lower bound for the scalar curvature of non-flat and non-compact expanding gradient Ricci soliton provided that the scalar curvature is non-negative and the potential function is proper. We also give an upper bound for the…

We construct new examples of manifolds of positive Ricci curvature which, topologically, are vector bundles over compact manifolds of almost nonnegative Ricci curvature. In particular, we prove that if E is the total space of a vector…

We mainly study 3-dimensional complete gradient Ricci solitons with positive sectional curvature, whose scalar curvature attains its maximum at some point. In section 2, we estimate the area growth of level sets and the volume growth of…

In $N(k)$-contact metric manifolds and/or $(k,\mu)$-manifolds, gradient Ricci solitons, compact Ricci solitons and Ricci solitons with $V$ pointwise collinear with the structure vector field $\xi $ are studied.

English translation of "Solitony Ricciego" (Wiadomo\'sci Matematyczne 48, 2012, no. 1, pp. 1-32). Despite the general-sounding title, the text covers just a few narrow topics: Perelman's proof of the fact that compact Ricci solitons are of…

We show that expanding K\"ahler-Ricci solitons which have positive holomorphic bisectional curvature and are asymptotic to K\"ahler cones at infinity must be the U(n)-rotationally symmetric expanding solitons constructed by Cao.