Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-27T19:45:25.550Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite type immersions of flat tori into Euclidean spaces

Published online by Cambridge University Press:  20 January 2009

Christos Baikoussis ,
Filip Defever ,
Themis Koufogiorgos  and
Leopold Verstraelen
Christos Baikoussis
Affiliation:
Department of Mathematics, University of Ionnina, Ionnina 45110, Greece
Filip Defever
Affiliation:
Instituut voor Theoretische Fysica, Celestijnenlaan 200 D, 3001 Heverleen, Belgium
Themis Koufogiorgos
Affiliation:
Department of Mathematics, University of Ionnina, Ionnina 45110, Greece
Leopold Verstraelen
Affiliation:
Departement Wiskunde, Celestijnenlaan 200 B, 3001 Heverleen, Belgium
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove the existence of nontrivial k-type surfaces by constructing k-type immersions of flat tori in 6 which are not product immersions.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 3 , October 1995 , pp. 413 - 420
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

REFERENCES

1.Baikoussis, C. and Blair, D., 2-type integral surfaces in S5(l), Tokyo J. Math. 14(2) (1991), 277–288.CrossRefGoogle Scholar
2.Baikoussis, C., Defever, F. and Koufogiorgos, T., Coordinate finite type integral surfaces in S5, Algebras, Groups, Geom. 10 (1993), 227–239.Google Scholar
3.Barros, M. and Chen, B.-Y., Stationary 2-type surfaces in a hypersphere, J. Math. Soc. Japan 39 (1987), 627–648.CrossRefGoogle Scholar
4.Chen, B.-Y., Total mean curvature and submanifolds of finite type (World Scientific, Singapore, 1984).CrossRefGoogle Scholar
5.Chen, B.-Y., Finite type submanifolds and Generalizations (University of Rome, Rome, 1985).Google Scholar
6.Chen, B.-Y., Some open problems and conjectures on submanifolds of finite type, Soochow J. Math. 17 (1991), 169–188.Google Scholar
7.Chen, B.-Y., Submanifolds of finite type and applications, in Proc. 2nd Intern. Geometry/Topology Workshops, Taegu (1992), 1–48.Google Scholar
8.Chen, B.-Y., Deprez, J., Dillen, F., Verstraelen, L. and Vrancken, L., Curves of finite type, in Geometry and Topology of Submanifolds II (1990), 76–110.Google Scholar
9.Garay, O., Spherical surfaces which are mass-symmetric and of 2-type, J. Geom. 33 (1988), 39–52.CrossRefGoogle Scholar
10.Kotani, M., A decomposition theorem of 2-type immersions, Nagoya Math. J. 118 (1990), 55–56.CrossRefGoogle Scholar
11.Miyata, Y., 2-type surfaces of constant curvature in Sn, Tokyo J. Math. 11 (1988), 157–204.CrossRefGoogle Scholar
12.Moore, J. D., Isometric immersions of Riemannian products, J. Differential Geom. 5 (1971), 159–168.CrossRefGoogle Scholar
13.Verstraelen, L., On submanifolds of finite Chen type and of restricted type, Results in Math. 20 (1991), 744–755.CrossRefGoogle Scholar