Conformal geometry of foliations

被引：26

作者：

Langevin, Remi ^{[1
]}

Walczak, Pawel G. ^{[2
]}

机构：

[1] Univ Bourgogne, Dijon, France

[2] Univ Lodz, PL-90131 Lodz, Poland

来源：

GEOMETRIAE DEDICATA | 2008年 / 132卷 / 01期

关键词：

foliation; conformal invariants; Dupin cyclide; totally umbilical leaves; spherical two piece property;

D O I：

10.1007/s10711-007-9213-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we begin a systematic study of conformal properties of codimension-1 foliations. We first define and study local conformal invariants. A case of particular interest is that of harmonic foliations of the plane. Then we study existence of totally umbilical and "Dupin" foliations on compact 3-manifolds of constant curvature.

引用

页码：135 / 178

页数：44

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