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Compact Gradient Shrinking Ricci Solitons with Positive Curvature Operator
Positive Curvature Operator Shrinking Ricci Solitons
2015/8/17
In this paper, we first derive several identities on a compact shrinking Ricci
soliton. We then show that a compact gradient shrinking soliton must be
Einstein, if it admits a Riemannian metri...
Bach-flat gradient steady Ricci solitons
Bach-flat gradient Ricci solitons Differential Geometry
2011/9/19
Abstract: In this paper we prove that any $n$-dimensional ($n\ge 4$) complete Bach-flat gradient steady Ricci solitons with positive Ricci curvature is isometric to the Bryant soliton. We also show th...
Some geometric analysis on generic Ricci solitons
Ricci solitons X–Laplacian scalar curvature estimates maximum principles volume estimates
2011/9/6
Abstract: We study the geometry of complete generic Ricci solitons with the aid of some geometric-analytical tools extending techniques of the usual Riemannian setting.
In this paper we establish three basic equations for a general soliton structure on the Riemannian manifold (M, h , i). We then draw some geometric conclusions with the aid of the maximum principle.