THE FORM OF THE COMPLETE SURFACES OF CONSTANT MEAN CURVATURE

Authors

  • Abdel Radi Abdel Rahman Abdel Gadir Department of Mathematics, Faculty of Education, Omdurman Islamic University, Omdurman, Sudan
  • Abdelhalim Zaied Elawad Faread Department of Mathematics, Faculty of Education, Omdurman Islamic University, Omdurman, Sudan
  • Adel AhmedHassan Kubba Department of Mathematics, Faculty of Education, Nile Valley University, Atbara, Sudan
  • Mohammed Iesa Mohammed Abker Department of Mathematics, Faculty of Education, Dalanj University, Dalanj, Sudan

DOI:

https://doi.org/10.53555/ms.v8i9.2127

Abstract

We explained and classified the complete surfaces of constant mean curvature in addition to construct the first examples of complete surface of positive curvature, properly embedded minimal surfaces and we prove that every complete connected immersed surface with positive extrinsic curvature  in  must be properly embedded, homeomorphic to a sphere or a plane. We followed the analytical mathematical method and we found that the complete surface of positive curvature has multi applications in different fields of science specially in physics.

 

 

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References

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Mark Walsh, Metric of Positive Scalar Curvature and Generalised Morse Functions, Part 1, Volume 209, 2011.

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P. Hartman, L. Nirenberg, on spherical images whose jacobians do not change signs, Amer . J. Math 81 (1959), (901)-920

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SorinDragomir – Giuseppe Tomassini, Differential Geometry and Analysis on CR Manifolds, Birkha ̈user Boston, USA, 2006.

Yu Aminov, Differential Geometry and Topology of Curves, CRC Press, 2000.

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Published

2022-09-22

How to Cite

Abdel Rahman Abdel Gadir , A. R. ., Zaied Elawad Faread, A. ., AhmedHassan Kubba, A. ., & Iesa Mohammed Abker, M. . (2022). THE FORM OF THE COMPLETE SURFACES OF CONSTANT MEAN CURVATURE. International Journal For Research In Mathematics And Statistics, 8(9), 1–4. https://doi.org/10.53555/ms.v8i9.2127

Issue

Vol. 8 No. 9 (2022): International Journal For Research In Mathematics And Statistics (ISSN: 2208-2662)

Section

Articles

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