Nontrivial breathers for Ricci flow

A Remark on Ricci Breathers and Solitons

In this article we give a brief survey of breather and soliton solutions to the Ricci flow and prove a no breather and soliton theorem for homogeneous solutions.

A Simple Proof on the Non-existence of Shrinking Breathers for the Ricci Flow

Suppose M is a compact n-dimensional manifold, n ≥ 2, with a metric gij(x, t) that evolves by the Ricci flow ∂tgij = −2Rij in M × (0, T ). We will give a simple proof of a recent result of Perelman on the non-existence of shrinking breather without using the logarithmic Sobolev inequality. It is known that Ricci flow is a very powerful tool in understanding the geometry and structure of manifol...

Ricci Lower Bound for Kähler–ricci Flow

The Ricci Flow for Nilmanifolds

We consider the Ricci flow for simply connected nilmanifolds, which translates to a Ricci flow on the space of nilpotent metric Lie algebras. We consider the evolution of the inner product with respect to time and the evolution of structure constants with respect to time, as well as the evolution of these quantities modulo rescaling. We set up systems of O.D.E.’s for some of these flows and des...

Ricci Flow Gravity

A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gravity. In particular there is no adjustable coupling constant. For the solar ...