2012/10/14 by Jinwen Yan, Yan, Jinwen, Fangyang Zheng +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.DG
paper · pdf · doi:10.48550/arxiv.1210.3774
12 pages
arxiv created 2012/10/14 · openalex publication_date 2012/10/14 · arxiv updated 2012/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1991, Dajczer and Rodriguez proved in [10] that a complete minimal real Kahler submanifold of codimension 2, if with complex dimension > 2, would be either holomorphic, or a cylinder, or complex ruled. In this article, we generalize their result to real analytic complete real Kahler submanifolds of codimension 4. The conclusion is that such the submanifold, if with complex dimension > 4, would be either partially holomorphic, or a cylinder, or a twisted cylinder in the sense that the complex relative nullity foliation is contained in a strictly larger holomorphic foliation, whose leaves are cylinders. We also examine the question of when such a submanifold is complex ruled.