Honam Mathematical Journal (호남수학학술지)

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CMC SURFACES FOLIATED BY ELLIPSES IN EUCLIDEAN SPACE E3

  • Ali, Ahmad Tawfik (Department of Mathematics, Faculty of Science, King Abdul Aziz University)
  • Received : 2018.05.03
  • Accepted : 2018.08.28
  • Published : 2018.12.25
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Abstract

In this paper, we will study the constant mean curvature (CMC) surfaces foliated by ellipses in three dimensional Euclidean space $E^3$. We prove that: (1): Surfaces foliated by ellipses are CMC surfaces if and only if it is a part of generalized cylinder. (2): All surfaces foliated by ellipses are not minimal surfaces. (3): CMC surfaces foliated by ellipses are developable surfaces. (4): CMC surfaces foliated by ellipses are translation surfaces generated by a straight line and plane curve.

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References

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