Surfaces with parallel mean curvature in Sasakian space forms

2013/08/30 by Dorel Fetcu, Fetcu, Dorel, Harold Rosenberg +1
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1308.6827

22 pages

arxiv created 2013/08/30 · openalex publication_date 2013/08/30 · arxiv updated 2013/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the global geometry of surfaces in Sasakian space forms whose mean curvature vector is parallel in the normal bundle (these include the Riemannian Heisenberg space of dimension 2n+1). We prove a codimension reduction theorem. We introduce two holomorphic quadratic differentials on anti-invariant such surfaces and use them to obtain classification theorems.

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