ﻻ يوجد ملخص باللغة العربية
By extending Koisos examples to the non-compact case, we construct complete gradient Kahler-Ricci solitons of various types on certain holomorphic line bundles over compact Kahler-Einstein manifolds. Moreover, a uniformization result on steady gradient Kahler-Ricci solitons with non-negative Ricci curvature is obtained under additional assumptions.
The main purpose of this article is to provide an alternate proof to a result of Perelman on gradient shrinking solitons. In dimension three we also generalize the result by removing the $kappa$-non-collapsing assumption. In high dimension this new m
We define virtual immersions, as a generalization of isometric immersions in a pseudo-Riemannian vector space. We show that virtual immersions possess a second fundamental form, which is in general not symmetric. We prove that a manifold admits a vir
A Ricci soliton $(M,g,v,lambda)$ on a Riemannian manifold $(M,g)$ is said to have concurrent potential field if its potential field $v$ is a concurrent vector field. Ricci solitons arisen from concurrent vector fields on Riemannian manifolds were stu
In this short note we prove that, in dimension three, flat metrics are the only complete metrics with non-negative scalar curvature which are critical for the $sigma_{2}$-curvature functional.
The aim of this paper is to prove some classification results for generic shrinking Ricci solitons. In particular, we show that every three dimensional generic shrinking Ricci soliton is given by quotients of either $mathds{S}^3$, $erretimesmathds{S}