The CR Immersion into a Sphere with the Degenerate CR Gauss Map

Wanke Yin; Yuan Yuan; Yuan Zhang

doi:10.1007/s12220-019-00154-x

The CR Immersion into a Sphere with the Degenerate CR Gauss Map

Wanke Yin, Yuan Yuan, Yuan Zhang

Department of Mathematics

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

1 Scopus citations

Abstract

It is a classical problem in algebraic geometry to characterize the algebraic subvariety by using the Gauss map. In this note, we study the analogous phenomenon 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.

Original language	English (US)
Pages (from-to)	526-550
Number of pages	25
Journal	Journal of Geometric Analysis
Volume	30
Issue number	1
DOIs	https://doi.org/10.1007/s12220-019-00154-x
State	Published - Jan 1 2020

Keywords

Degeneracy rank
Degenerate Gauss map
Geometric rank
Normal form
Proper holomorphic map

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s12220-019-00154-x

Cite this

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KW - Geometric rank

KW - Normal form

KW - Proper holomorphic map

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The CR Immersion into a Sphere with the Degenerate CR Gauss Map

Abstract

Keywords

ASJC Scopus subject areas

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