Holomorphic Euler number of Kahler manifolds with almost nonnegative Ricci curvature

2019/09/10 by Xiaoyang Chen, Chen, Xiaoyang
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1909.05116

openalex publication_date 2019/09/10 · openalex created_date 2019/09/19 · openalex updated_date 2026/07/28

Abstract

Let Mⁿ be a compact Kahler manifold with almost nonnegative Ricci curvature and nonzero first Betti number. We show that the holomorphic Euler number of Mⁿ vanishes, which gives a new obstruction for compact complex manifolds admitting Kahler metrics with almost nonnegative Ricci curvature. A crucial step in the proof is to show a vanishing theorem of Dolbeault-Morse-Novikov cohomology.

Citations

• Morse-Novikov cohomology of locally conformally Kähler surfaces

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