Results Related to the Chern-Yamabe Flow
- 주제(키워드) 도움말 Chern-Yamabe problem , Chern-Yamabe flow , Chern scalar curvature
- 발행기관 SPRINGER
- 발행년도 2021
- 총서유형 Journal
- 본문언어 영어
초록/요약 도움말
Let (X, omega(0)) be a compact complex manifold of complex dimension n endowed with a Hermitian metric omega(0). The Chern-Yamabe problem is to find a conformal metric of omega(0) such that its Chern scalar curvature is constant. As a generalization of the Chern-Yamabe problem, we study the problem of prescribing Chern scalar curvature. We then estimate the first nonzero eigenvalue of Hodge-de Rham Laplacian of (X, omega(0)). On the other hand, we prove a version of conformal Schwarz lemma on (X, omega(0)). All these are achieved by using geometric flows related to the Chern-Yamabe flow. Finally, we prove the backwards uniqueness of the Chern-Yamabe flow.
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