Conformal Geometry Solitons

Abstract:

In this paper, we deal with a generalization of the Yamabe flow named conformal geometry flow. Firstly we derive a monotone formula of the Einstein-Hilbert functional under the conformal geometry flow. Then we prove the properties that the conformal geometry solitons and conformal geometry breather both have constant scalar curvature at each time by using the modified Einstein-Hilbert function. Finally we present some properties of Yamabe solitons in compact manifold and noncompact manifolds through the equation of Yamabe soliton.

• Periodical: Advanced Materials Research (Volumes 472-475)
• Pages: 123-126
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.472-475.123
• Online since: February 2012
• Authors: Rong Rong Cao, Xiang Gao
• Keywords: Conformal Geometry Soliton, Einstein-Hilbert Function, Yamabe Flow

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