Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SURFACES FOLIATED BY ELLIPSES WITH CONSTANT GAUSSIAN CURVATURE IN EUCLIDEAN 3-SPACE

  • Ali, Ahmed T. (Department of Mathematics, Faculty of Science, King Abdul Aziz University) ;
  • Hamdoon, Fathi M. (Mathematics Department, Faculty of Science, Al-Azhar University)
  • Received : 2017.09.21
  • Accepted : 2017.11.21
  • Published : 2017.12.30
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Abstract

In this paper, we study the surfaces foliated by ellipses in three dimensional Euclidean space ${\mathbf{E}}^3$. We prove the following results: (1) The surface foliated by an ellipse have constant Gaussian curvature K if and only if the surface is flat, i.e. K = 0. (2) The surface foliated by an ellipse is a flat if and only if it is a part of generalized cylinder or part of generalized cone.

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References

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Cited by

  1. CMC SURFACES FOLIATED BY ELLIPSES IN EUCLIDEAN SPACE E3 vol.40, pp.4, 2017, https://doi.org/10.5831/hmj.2018.40.4.701