We propose a flow to study the Chern-Yamabe problem and discuss the long time existence of the flow. In the balanced case we show that the Chern-Yamabe problem is the Euler-Lagrange equation of some functional. The monotonicity of the functional along the flow is derived. We also show that the functional is not bounded from below.
A note on Chern-Yamabe problem / Calamai, Simone; Zou, Fangyu. - In: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS. - ISSN 0926-2245. - ELETTRONICO. - 69:(2020), pp. 101612.0-101612.0. [10.1016/j.difgeo.2020.101612]
A note on Chern-Yamabe problem
Calamai, Simone
;
2020
Abstract
We propose a flow to study the Chern-Yamabe problem and discuss the long time existence of the flow. In the balanced case we show that the Chern-Yamabe problem is the Euler-Lagrange equation of some functional. The monotonicity of the functional along the flow is derived. We also show that the functional is not bounded from below.
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