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arXiv · 1211.4513

An asymptotically cusped three dimensional expanding gradient Ricci soliton

Daniel Ramos
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Abstract

We construct an expanding gradient Ricci soliton in dimension three over the topological manifold R x T^2 (the product of a line and a torus) that aproaches asymptotically a constant curvature cusp at one end, and a flat manifold on the other end. We prove that this is the only gradient soliton with this topology, provided the curvature is negatively pinched, -1/4 < sec < 0, at the time-zero manifold (normalizing the soliton to be born at time -1).

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Daniel Ramos. 2013-01-10. An asymptotically cusped three dimensional expanding gradient Ricci soliton. https://arxiv.org/abs/1211.4513

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