Renormalized characteristic forms of the Cheng--Yau metric and global CR\n invariants

2019/12/23 by Taiji Marugame, Marugame, Taiji
Mathematics · #32V05 (Primary) #53A55 (Secondary) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1912.10684

openalex publication_date 2019/12/23 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

For each invariant polynomial \Φ, we construct a global CR invariant via\nthe renormalized characteristic form of the Cheng--Yau metric on a strictly\npseudoconvex domain. When the degree of \Φ is 0, the invariant agrees with\nthe total Q'-curvature. When the degree is equal to the CR dimension, we\nconstruct a primed pseudo-hermitian invariant \I'_\Φ which\nintegrates to the corresponding CR invariant. These are generalizations of the\n\I'-curvature on CR five-manifolds, introduced by Case--Gover.\n

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