Nihonkai Mathematical Journal

Remarks on the Set of Poles on a Pointed Complete Surface

Toshiro Soga

Full-text: Open access

Abstract

M. Tanaka ([2]) determined the radius of the ball which consists of all poles in a von Mangoldt surface of revolution. The purpose of the present paper is to give an alternative proof and a geometrical meaning of the radius. Furthermore, we estimate the radius of the maximal ball consisting of poles in a complete surface homeomorphic to the plane under a certain condition.

Article information

Source
Nihonkai Math. J., Volume 22, Number 1 (2011), 23-37.

Dates
First available in Project Euclid: 14 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.nihmj/1339694048

Mathematical Reviews number (MathSciNet)
MR2894023

Zentralblatt MATH identifier
1250.53006

Subjects
Primary: 53C22: Geodesics [See also 58E10]

Keywords
Geodesic pole disconjugate property surface of revolution

Citation

Soga, Toshiro. Remarks on the Set of Poles on a Pointed Complete Surface. Nihonkai Math. J. 22 (2011), no. 1, 23--37. https://projecteuclid.org/euclid.nihmj/1339694048


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References

  • P. Hartman, Ordinary differential equations, Wiley, New York, 1964.
  • M. Tanaka, On a characterization of a surface of revolution with many poles, Mem. Fac. Sci., Kyushu Univ. Series A, Mathematics 46 (2) (1992), 251–268.
  • M. Tanaka, On the cut loci of a von Mangoldt's surface of revolution, J. Math. Soc. Japan 44 (4) (1992), 631–641.
  • H. von Mangoldt, Uber diejenigen Punkte auf positive gekrümmten Flähen, welche die Eigenshaft haben, dass die von ihnen ausgehenden geodätischen Linien aufhören kürzeste Linien zu siein, J. Reine. Angew. Math. 91 (1881), 23–53.