Complete lifts of harmonic maps and morphisms between Euclidean spaces

1995/11/07 by Ye‐Lin Ou, Ye-lin Ou, Ou, Ye-lin
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9511003

13 pages, AMS-Latex, no figures

arxiv created 1995/11/07 · openalex publication_date 1995/11/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the complete lifts of maps between (real and complex) Euclidean spaces and study their properties concerning holomorphicity, harmonicity and horizontal weakly conformality. As applications, we are able to use this concept to characterize holomorphic maps ϕ:\Bbb C^m⊃ U\longrightarrow \Bbb Cⁿ (Proposition 2.3) and to construct many new examples of harmonic morphisms (Theorem 3.3). Finally we show that the complete lift of the quaternion product followed by the complex product is a simple and explicit example of a harmonic morphism which does not arise (see Definition 4.8 in \citeBaiWoo95) from any Kähler structure.

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