Flatness of CR submanifolds in a sphere

Shan Yu Ji; Yuan Yuan

doi:10.1007/s11425-010-0052-4

Flatness of CR submanifolds in a sphere

Shan Yu Ji, Yuan Yuan

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In Euclidean geometry, for a real submanifold M in E^n+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 ℂP^n+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.

Original language	English (US)
Pages (from-to)	701-718
Number of pages	18
Journal	Science China Mathematics
Volume	53
Issue number	3
DOIs	https://doi.org/10.1007/s11425-010-0052-4
State	Published - 2010
Externally published	Yes

Keywords

CR second fundamental form
CR submanifolds
Proper holomorphic mappings between balls
Sphere

ASJC Scopus subject areas

General Mathematics

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10.1007/s11425-010-0052-4

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AU - Ji, Shan Yu

AU - Yuan, Yuan

PY - 2010

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AB - 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.

KW - CR second fundamental form

KW - CR submanifolds

KW - Proper holomorphic mappings between balls

KW - Sphere

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Flatness of CR submanifolds in a sphere

Abstract

Keywords

ASJC Scopus subject areas

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