Gradient Einstein solitons

Details Gradient Einstein solitons Gradient Einstein solitons

2012-01-31

arxiv.org/abs/1201.6620v2

Mathematics

Differential Geometry

some references added

Scientific paper

In this paper we introduce the notion of gradient Einstein solitons as self-similar solutions of the gradient flow associated to the Einstein-Hilbert action. After proving the rectifiability of $f$, we use it to investigate the geometric properties of the solitons. In particular, we show that there is only one complete three-dimensional gradient steady Einstein soliton with positive sectional curvature. This solution is rotationally symmetric and asymptotically cylindrical. Hence, it represents the analogue of the Hamilton's cigar in dimension three. We also consider the class of gradient solitons associated to the flows $\partial_t g = -2(Ric -\rho R\,g)$, for any constant $\rho\neq 0$. In particular, for $\rho=1/2(n-1)$, we classify all complete three-dimensional gradient Schouten solitons in the steady case as well as in the shrinking case.

Affiliated with

Also associated with

No associations

Rating

Gradient Einstein solitons does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Gradient Einstein solitons, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gradient Einstein solitons will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-57496