In Euclidean geometry, for a real submanifold M in En+a, M is a piece of En if and only if its second fundamental form is identically zero. In projective geometry, for a complex submanifold M in ℂPn+a, M is a piece of ℂℚn if and only if its projective second fundamental form is identically zero. In CR geometry, we prove the CR analogue of this fact in this paper.
- CR second fundamental form
- CR submanifolds
- Proper holomorphic mappings between balls
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