On complete gradient steady Ricci solitons with vanishing
نویسندگان
چکیده
In this paper, we extend the work of Cao-Chen [9] on Bach-flat gradient Ricci solitons to classify $n$-dimensional ($n\ge 5$) complete $D$-flat steady solitons. More precisely, prove that any noncompact soliton with vanishing $D$-tensor is either Ricci-flat, or isometric Bryant soliton. Furthermore, proof extends shrinking case and expanding as well.
منابع مشابه
On Complete Gradient Shrinking Ricci Solitons
In this paper we derive a precise estimate on the growth of potential functions of complete noncompact shrinking solitons. Based on this, we prove that a complete noncompact gradient shrinking Ricci soliton has at most Euclidean volume growth. The latter result can be viewed as an analog of the well-known theorem of Bishop that a complete noncompact Riemannian manifold with nonnegative Ricci cu...
متن کاملGeometry of Complete Gradient Shrinking Ricci Solitons
The notion of Ricci solitons was introduced by Hamilton [24] in mid 1980s. They are natural generalizations of Einstein metrics. Ricci solitons also correspond to self-similar solutions of Hamilton’s Ricci flow [22], and often arise as limits of dilations of singularities in the Ricci flow. In this paper, we will focus our attention on complete gradient shrinking Ricci solitons and survey some ...
متن کاملOn Locally Conformally Flat Gradient Steady Ricci Solitons
In this paper, we prove that a complete noncompact non-flat conformally flat gradient steady Ricci soliton is, up to scaling, the Bryant soliton. 1. The result A complete Riemannian metric gij on a smooth manifold M n is called a gradient steady Ricci soliton if there exists a smooth function F on M such that the Ricci tensor Rij of the metric gij is given by the Hessian of F : Rij = ∇i∇jF. (1....
متن کاملOn Gradient Ricci Solitons with Symmetry
We study gradient Ricci solitons with maximal symmetry. First we show that there are no non-trivial homogeneous gradient Ricci solitons. Thus the most symmetry one can expect is an isometric cohomogeneity one group action. Many examples of cohomogeneity one gradient solitons have been constructed. However, we apply the main result in [12] to show that there are no noncompact cohomogeneity one s...
متن کاملGradient Kähler Ricci Solitons
Some observations about the local and global generality of gradient Kähler Ricci solitons are made, including the existence of a canonically associated holomorphic volume form and vector field, the local generality of solutions with a prescribed holomorphic volume form and vector field, and the existence of Poincaré coordinates in the case that the Ricci curvature is positive and the vector fie...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2021
ISSN: ['2330-1511']
DOI: https://doi.org/10.1090/proc/15317