(11007) Generalized Ricci flow I: Local existence and uniqueness

来源:数学科学研究中心

Abstract
In this paper we investigate a kind of generalized Ricci flow which possesses a gradient form. We study the monotonicity of the given function under the generalized Ricci flow and prove that the related system of par-
tial differential equations are strictly and uniformly parabolic. Based on this, we show that the generalized Ricci flow defined on a n-dimensional compact Riemannian manifold admits a unique short-time smooth solution. Moreover, we also derive the evolution equations for the curvatures, which play an important role in our future study.
Key words and phrases: Generalized Ricci flow, uniformly parabolic system, short-time existence, Thurston’s eight geometries.

  • 1107.3270v1.pdf