Non-umbilical quaternionic contact hypersurfaces in hyper-K "ahler\n manifolds

2016/09/09 by Stefan Ivanov, Ivan Minchev, Ivanov, Stefan +3
Mathematics · #53C17 #58G30 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1609.02838

openalex publication_date 2016/09/09 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We show that any compact quaternionic contact (qc) hypersurfaces in a\nhyper-K "ahler manifold which is not totally umbilical has an induced qc\nstructure, locally qc homothetic to the standard 3-Sasakian sphere. We also\nshow that any nowhere umbilical qc hypersurface in a hyper-K "ahler manifold is\nendowed with an involutive 7-dimensional distribution whose integral leafs are\nlocally qc-conformal to the standard 3-Sasakian sphere.\n

Related

• Quaternionic contact hypersurfaces in hyper-Kähler manifolds
• Quaternionic contact structure with integrable complementary distribution
• The qc Yamabe problem on non-spherical quaternionic contact manifolds
• The Obata sphere theorems on a quaternionic contact manifold of\n dimension bigger than seven
• Quaternionic contact Einstein manifolds