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. China

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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.

  • [1] Dillen, F., Mys, G., Verstraelen, L., Vrancken, L. 1994 The affine mean curvature vector for surfaces in R4 Math. Nachr. 166 155165 .

  • [2] Hou, Z.-H., Fu, Y. 2009 Flat affine maximal surfaces in R4 Result. Math. 55 389400 .

  • [3] Li, J. 1999 Harmonic surfaces in affine 4-space Internat. J. Math. 10 523528.

  • [4] Magid, M., Scharlach, C., Vrancken, L. 1995 Affine umbilical surfaces in R4 Manuscripta Math. 88 275289 .

  • [5] Magid, M., Vrancken, L. 2000 Flat affine surfaces in R4 with flat normal connection Geom. Dedicata 81 1931 .

  • [6] Magid, M., Vrancken, L. 1999 Affine translation surfaces Result. Math. 35 134144.

  • [7] Martínez, A., Milán, F. 1995 Affine definite 2-spheres in R4 Geometry and Topology of Submanifolds VII World Scientific Singapore 182185.

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  • [8] Martínez, A., Milán, F. 1995 A characterization of the complex paraboloid Result. Math. 27 302307.

  • [9] Nomizu, K., Sasaki, T. 1994 Affine Differential Geometry: Geometry of Affine Immersions Cambridge University Press Cambridge, New York.

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  • [10] Nomizu, K., Vrancken, L. 1993 A new equiaffine theory for surfaces in R4 Internat. J. Math. 4 127165 .

  • [11] Scharlach, C., Affine Geometry of Surfaces and Hypersurfaces in R4, Habilitation Thesis, Fac. II, TU Berlin (2006).

  • [12] Verstraelen, L., Vrancken, L., Witowicz, P. 2000 Indefinite affine umbilical surfaces in R4 Geom. Dedicata 79 109119 .

  • [13] Vrancken, L. 1995 Affine surfaces whose geodesics are planar curves Proc. Amer. Math. Soc. 123 38513854 .

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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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