Journal of Mathematics (Jan 2021)

A PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ2 into ℝ4

  • Mor Dione,
  • Bira Gaye Diop,
  • Athoumane Niang

DOI
https://doi.org/10.1155/2021/2012354
Journal volume & issue
Vol. 2021

Abstract

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A simple interpretation of the PDE for isometric immersion of the hyperbolic plane ℍ2 into ℝ4 is given. Thus, necessary and sufficient conditions are obtained. And, under natural additional conditions, we show that there are no complete solutions, but we can have special local solutions.