Acta Mathematica Hungarica
Volume/Issue:
Volume 131: Issue 1-2
A characterization of affine spheres in R4
Authors:
Yu Fu Department of Mathematics, Dalian Nationalities University, Dalian 116600, P. R. China

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Zhong Hua Hou School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. Chinae-mail: zhhou@dlut.edu.cn

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Pages:
160–173
Online Publication Date:
11 Jan 2011
Publication Date:
01 Apr 2011
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-010-0044-4
Keywords:
equiaffine normal bundle; affine sphere; affine mean curvature vector; 53A15
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Abstract

A surface immersed in R4 is called a proper affine sphere if the position vector belongs to the affine normal plane. We classify proper affine spheres with ∇⊥g⊥=0 whose affine mean curvature vector has constant length. Moreover, we find some concrete examples of affine spheres which are not affine umbilical.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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