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Surfaces with isometric geodesics

Published online by Cambridge University Press:  20 January 2009

C. Charitos  and
P. Pamfilos
C. Charitos
Affiliation:
University of CreteDepartment Of MathematicsIraklion P.O. Box 470Greece
P. Pamfilos
Affiliation:
University of CreteDepartment Of MathematicsIraklion P.O. Box 470Greece
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Abstract

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The aim of the paper is to prove the Theorem: Let M be a surface in the euclidean space E3 which is diffeomorphic to the sphere and suppose that all geodesies of M are congruent. Then M is a euclidean sphere.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 3 , October 1991 , pp. 359 - 362
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

REFERENCES

1.Besse, A., Manifolds all of Whose Geodesies are Closed (Springer-Verlag, 1978).CrossRefGoogle Scholar
2.Freedman, M., Hass, J. and Scott, P., Closed Geodesies on Surfaces. Preprint, Liverpool University, 11 1981.Google Scholar
3.Lingeberg, W. K., Lectures on Closed Geodesies (Springer-Verlag, 1978).Google Scholar
4.Lusternik, L., The Topology of Function Spaces and the Calculus of Variations in the Large, Translations of Math. Monographs, Vol. 16, Providence, R.I., 1966.Google Scholar
5.Milnor, J., Analytic proofs of the hairy ball theorem, Am. Math. Monthly 85 (1978).Google Scholar