2013/11/22 by Antonio J. Di Scala, Francisco Vittone, Di Scala, Antonio J. +1
Mathematics · #53B15 #53B25 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Point processes and geometric inequalities #math.DG #msc:53B15 #msc:53B25
paper · pdf · doi:10.48550/arxiv.1311.5778
openalex publication_date 2013/11/22 · arxiv created 2015/05/04 · arxiv updated 2015/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a CR-submanifold of a complex space form. We complete the local classification of normal holonomies for complex submanifolds. We show that the normal holonomy group of a coisotropic submanifold acts as the holonomy representation of a Riemannian symmetric space. In case of a totally real submanifold we give two results about reduction of codimension. We describe explicitly the action of the normal holonomy in the case in which the totally real submanifold is contained in a totally real totally geodesic submanifold. In such a case we prove the compactness of the normal holonomy group.