On Chern-Yamabe problem

By Daniele Angella, Simone Calamai, Cristiano Spotti. 2015

53 citations recorded by the source corpus.

We initiate the study of an analogue of the Yamabe problem for complex manifolds. More precisely, fixed a conformal Hermitian structure on a compact complex manifold, we are concerned in the existence of metrics with constant Chern scalar curvature. In this note, we set the problem and we provide a positive answer when the expected constant Chern scalar curvature is non-positive. In particular, this includes the case when the Kodaira dimension of the manifold is non-negative. Finally, we give some remarks on the positive curvature case, showing existence in some special cases and the failure, in general, of uniqueness of the solution.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/02bdf7e80b27206b5cf3dcae149c764673ccfcd9

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In Applied Mathematics

1. Xiaokui Yang
2. Fang Zheng
3. Valentino Tosatti
4. Lei Ni

In Geometry and Topology

1. Xiaokui Yang
2. Fang Zheng
3. Valentino Tosatti
4. Lei Ni

Citations in the corpus

• Scalar curvature on compact complex manifolds (2017, background): “lows from Claim 1 and Claim 2. The proof of Theorem 1.1 is completed. Before giving the proof of Theorem 1.3, we need the following results which follow from Gauduchon’s conformal method. We refer to [2, 3, 1, 9, 10] for more details. See also an almost Hermitian version investigated in [12]. For re”