Metrics of Poincaré type with constant scalar curvature: a topological constraint

Details Metrics of Poincaré type with constant scalar curvature: a topological constraint Metrics of Poincaré type with constant scalar curvature: a topological constraint

2011-10-20

arxiv.org/abs/1110.4548v1

Mathematics

Differential Geometry

20 pages

Scientific paper

Let D a divisor with simple normal crossings in a Kahler manifold X. The purpose of this short note is to show that the existence of a Poincare type metric with constant scalar curvature in on the complement of D implies for any component of the divisor that the scalar curvature of Poincare type metric outside of D is less than the mean scalar curvature attached to the component. We also explain how those results were already conjectured by G. Szekelyhidi when D is reduced to one component.

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