2014/11/27 by Toru Sasahara, Sasahara, Toru
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1411.7470
openalex publication_date 2014/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of Lagrangian H-umbilical submanifolds was introduced by B. Y. Chen in 1997, and these submanifolds have appeared in several important problems in the study of Lagrangian submanifolds from the Riemannian geometric point of view. Recently, the author introduced the notion of tangentially biharmonic submanifolds, which are defined as submanifolds such that the bitension field of the inclusion map has vanishing tangential component. The normal bundle of a round hypersphere in ℝn can be immersed as a tangentially biharmonic Lagrangian H-umbilical submanifold in ℂn. Motivated by this fact, we classify tangentially biharmonic Lagrangian H-umbilical submanifolds in complex space forms.