Open AccessA PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane into
Author(s) -
Mor Dione,
Bira Gaye Diop,
Athoumane Niang
Publication year - 2021
Publication title -
journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.252
H-Index - 13
eISSN - 2314-4785
pISSN - 2314-4629
DOI - 10.1155/2021/2012354
Subject(s) - mathematics , isometric exercise , immersion (mathematics) , upper half plane , combinatorics , pure mathematics , medicine , physical therapy
A simple interpretation of the PDE for isometric immersion of the hyperbolic plane ℍ 2 into ℝ 4 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.
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