Homogeneous surfaces in Lie sphere geometry

Tongzhu Li

doi:10.1007/s10711-010-9460-4

Homogeneous surfaces in Lie sphere geometry

Tongzhu Li^*

^*Corresponding author for this work

School of Mathematics and Statistics

Capital Normal University

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

1 Citation (Scopus)

Abstract

In this paper, we study surfaces of S³ in the context of Lie sphere geometry. We construct invariants with respect to Lie sphere transformations on the surfaces, which determine the surfaces up to a Lie sphere transformation. Finally we classify completely the homogeneous surfaces in S³ with respect to the Lie sphere transformation group of S³.

Original language	English
Pages (from-to)	15-43
Number of pages	29
Journal	Geometriae Dedicata
Volume	149
Issue number	1
DOIs	https://doi.org/10.1007/s10711-010-9460-4
Publication status	Published - Dec 2010

Keywords

Canal surface
Lie homogeneous surface
Lie sphere geometry

Access to Document

10.1007/s10711-010-9460-4

Cite this

@article{1de0177d3ff748bda6296af31bfc6cae,

title = "Homogeneous surfaces in Lie sphere geometry",

abstract = "In this paper, we study surfaces of S3 in the context of Lie sphere geometry. We construct invariants with respect to Lie sphere transformations on the surfaces, which determine the surfaces up to a Lie sphere transformation. Finally we classify completely the homogeneous surfaces in S3 with respect to the Lie sphere transformation group of S3.",

keywords = "Canal surface, Lie homogeneous surface, Lie sphere geometry",

author = "Tongzhu Li",

year = "2010",

month = dec,

doi = "10.1007/s10711-010-9460-4",

language = "English",

volume = "149",

pages = "15--43",

journal = "Geometriae Dedicata",

issn = "0046-5755",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Homogeneous surfaces in Lie sphere geometry

AU - Li, Tongzhu

PY - 2010/12

Y1 - 2010/12

N2 - In this paper, we study surfaces of S3 in the context of Lie sphere geometry. We construct invariants with respect to Lie sphere transformations on the surfaces, which determine the surfaces up to a Lie sphere transformation. Finally we classify completely the homogeneous surfaces in S3 with respect to the Lie sphere transformation group of S3.

AB - In this paper, we study surfaces of S3 in the context of Lie sphere geometry. We construct invariants with respect to Lie sphere transformations on the surfaces, which determine the surfaces up to a Lie sphere transformation. Finally we classify completely the homogeneous surfaces in S3 with respect to the Lie sphere transformation group of S3.

KW - Canal surface

KW - Lie homogeneous surface

KW - Lie sphere geometry

UR - http://www.scopus.com/inward/record.url?scp=78149495385&partnerID=8YFLogxK

U2 - 10.1007/s10711-010-9460-4

DO - 10.1007/s10711-010-9460-4

M3 - Article

AN - SCOPUS:78149495385

SN - 0046-5755

VL - 149

SP - 15

EP - 43

JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 1

ER -

Homogeneous surfaces in Lie sphere geometry

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this