Flatness of CR Submanifolds in a Sphere

Abstract

Let $M$ be the image of a smooth CR embedding of a strictly pseudoconvex CR real hypersurface into a sphere. If the CR second fundamental form of $M$ vanishes, we show that $M$ is a totally geodesic submanifold.

Dedicated to Professor Yang, Lo on the Occasion of his 70th Birthday

References in corpus (2)

• Obstructions to embeddability into hyperquadrics and explicit examples
• A gap rigidity for proper holomorphic maps from $ \B^{n+1}$ to $ \B^{3n-1}$

Cited by in corpus (3)

• The CR Ahlfors derivative and a new invariant for spherically equivalent CR maps
• Semi-isometric CR immersions of CR manifolds into Kähler manifolds and applications
• CR and Holomorphic Embeddings and Pseudo-conformally Flat Metrics