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Liouville Theorems for holomorphic maps on pseudo-Hermitian manifolds (2110.03238v1)
Published 7 Oct 2021 in math.DG and math.CV
Abstract: We prove some Liouville type results for generalized holomorphic maps in three classes: maps from pseudo-Hermitian manifolds to almost Hermitian manifolds, maps from almost Hermitian manifolds to pseudo-Hermitian manifolds and maps from pseudo-Hermitian manifolds to pseudo-Hermitian manifolds, assuming that the domains are compact. For instance, we show that any $(J,JN)$ holomorphic map from a compact pseudo-Hermitian manifold $M$ with nonnegative (resp. positive) pseudo-Hermitian sectional curvature to an almost Hermitian manifold $N$ with negative (resp. nonpositive) holomorphic sectional curvature is constant. We also construct explicit almost CR structures on a complex vector bundle over an almost CR manifold.