Kodaira dimension of almost K "ahler manifolds and curvature of the\n canonical connection

2019/08/29 by Andrea Cattaneo, Cattaneo, Andrea, Antonella Nannicini +3 · 1 citation
Mathematics · #53C25 #53C55 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1908.11328

openalex publication_date 2019/08/29 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

The notion of Kodaira dimension has recently been extended to general almost\ncomplex manifolds. In this paper we focus on the Kodaira dimension of almost\nK "ahler manifolds, providing an explicit computation for a family of almost\nK "ahler threefolds on the differentiable manifold underlying a Nakamura\nmanifold. We concentrate also on the link between Kodaira dimension and the\ncurvature of the canonical connection of an almost K "ahler manifold, and show\nthat in the previous example (and in another one obtained from a Kodaira\nsurface) the Ricci curvature of the almost K "ahler metric vanishes for all the\nmembers of the family.\n

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