Abstract
In Euclidean geometry, for a real submanifold M in \( \mathbb{E}^{n + a} \), M is a piece of \( \mathbb{E}^n \) 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.
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Dedicated to Professor Yang Lo on the Occasion of his 70th Birthday
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Ji, S., Yuan, Y. Flatness of CR submanifolds in a sphere. Sci. China Math. 53, 701–718 (2010). https://doi.org/10.1007/s11425-010-0052-4
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DOI: https://doi.org/10.1007/s11425-010-0052-4