Poles and Straight Lines on Surfaces
Main Article Content
Abstract
There are open problems originated from classical differential geometry. In this note some interesting open problems will be introduced.
Keywords: -
Corresponding author: E-mail: m-tanaka@sm.u-tokai.ac.jp
Article Details
Copyright Agreement Statement
The corresponding author has to submit Copyright Agreement form after the article is accepted for publication in order to warrant that this contribution is original and that he/she has full power to make this grant. The author signs for and accepts responsibility for releasing this material on behalf of any and all co-authors.
The author(s) grant Current Applied Science and Technology a non-exclusive, irrevocable, royalty-free license to publish, reproduce, distribute, and archive the article in print and electronic form with effect if and when the article is accepted for publication. In the event that the article is withdrawn prior to acceptance or is declined, this agreement shall have no effect, and no party shall be bound by it.
The author(s) retain copyright of this article, including but not limited to the right to reproduce and distribute the article, to include it in a thesis or book, and to post it on an institutional or personal repository, provided that the original publication in Current Applied Science and Technology is properly cited.
References
[2] M. Maeda, Geodesic spheres and poles, Geometry of Manifolds, Academic Press, MA, 1989, 281-293.
[3] H. von Mangodt, Über diejenigen Punkte auf positive gekrümmten Flächen, welche die Eingenschaft haben, dass die von Ihnen ausgehenden geodätischen Linien nie aufhören, kürzeste Linien zu sein, J. Reine. Angrew. Math. 91, (1881), 23-53.
[4] K. Shiohama, T. Shioya and M. Tanaka, The Geometry of Total Curvature on Complete Open Surfaces, Cambridge Tracts in Mathematics, No. 159. Cambridge University Press, (2003)
[5] R. Sinclair and M. Tanaka, Loki: Software for computing cut loci, Experimental Mathematics 11, (2002), 1-25.
[6] R. Sinclair and M. Tanaka, The set of poles of a two-sheeted hyperboloid, Experiment, Math. 11 (2002), 27-36.
[7] Sugahara, K., On the poles of Riemannian manifolds of nonnegative curvature, Progress in Differential Geometry, Advanced Studies in Pure Math., vol. 22 (1993), 321-332.
[8] M. Tanaka, On a characterization of a surface of revolution with many poles, Memoirs Fac. Sci. Kyushu Univ. Ser. A, 46 (1992), 251-268.