The CR immersion into a sphere with the degenerate CR Gauss map

2018/06/23 by Wanke Yin, Yuan Yuan, Yin, Wanke +3
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematics and Applications #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1806.08961

openalex publication_date 2018/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is a classical problem in algebraic geometry to characterize the algebraic subvariety by using the Gauss map. In this note, we try to develop the analogue theory in CR geometry. In particular, under some assumptions, we show that a CR map between spheres is totally geodesic if and only if the CR Gauss map of the image is degenerate.

Related

• Partial rigidity of degenerate CR embeddings into spheres
• Unique jet determination and extension of germs of CR maps into spheres
• The Gauss map and the dual variety of real-analytic submanifolds in a sphere or in a hyperbolic space
• Group-Invariant CR maps of the sphere \mathbbS⁵
• CR embedded submanifolds of CR manifolds