Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T13:39:05.241Z Has data issue: false hasContentIssue false
  • English
  • Français

Hypersurfaces of En+1 Satisfying Δx = Ax + B

Part of: Classical differential geometry Global differential geometry

Published online by Cambridge University Press:  09 April 2009

Th. Hasanis  and
Th. Vlachos
Th. Hasanis
Affiliation:
University of Ioannina45110 Ioannina, Greece
Th. Vlachos
Affiliation:
University of Ioannina45110 Ioannina, Greece
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 consider hypersurfaces of En+1 whose position vector x satisfies Δx = Ax + B, where Δ is the induced Laplacian, and prove that these are open parts of minimal hypersurfaces, hyperspheres or generalized circular cylinders.

MSC classification

Secondary: 53C40: Global submanifolds 53A05: Surfaces in Euclidean space
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 3 , December 1992 , pp. 377 - 384
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Dillen, F., Pas, J. and Verstraelen, L., ‘On surfaces of finite type in Euclidean 3-space’, Kodai Math. J. 13 (1990), 10–21.CrossRefGoogle Scholar
[2]Garay, O., ‘An extension of Takahashi's Theorem’, Geom. Dedicata 34 (1990), 105–112.CrossRefGoogle Scholar
[3]Takahashi, T., ‘Minimal immersions of Riemannian manifolds’, J. Math. Soc. Japan 18 (1966), 380–385.CrossRefGoogle Scholar