On the Entropy Formulas and Solitons for the Ricci-Harmonic Flow
Tóm tắt
This paper is concerned with entropy monotonicity formulas and classification of gradient almost soliton for Ricci-harmonic flow. The new entropy formulas introduced here are monotone in general along the flow and constant exactly on shrinker or expander as the case may be. The consequence of this is the nonexistence of periodic solutions except those that are gradient solitons. Furthermore, the paper discusses gradient almost Ricci-harmonic soliton with respect to a fixed metric, not minding the dynamical nature of the flow but treating the defining elliptic equations and relying on analytic techniques. Finally, we are able to classify gradient almost Ricci-harmonic solitons.
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