2022•International Journal For Research In Mathematics And StatisticsOpen access

THE FORM OF THE COMPLETE SURFACES OF CONSTANT MEAN CURVATURE

Abdel Radi Abdel Rahman Abdel Gadir, Abdelhalim Zaied Elawad Faread, Adel AhmedHassan Kubba, Mohammed Iesa Mohammed Abker

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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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Key concepts: Curvature, Mean curvature, Surface (topology), Constant curvature, Constant (computer programming), Constant-mean-curvature surface, Mathematics, Plane (geometry)