Asian Journal of Mathematics and Computer Research

ON THE ISOMETRIC IMMERSION OF THE LORENTZ-HEISENBERG GROUP H3 IN EUCLIDEAN SPACE ℝ4

FATIMA BOUDAOUD *

Laboratory of Mathematics and its Application, University Oran1 Ahmed Benbella, Algeria.

RACHIDA KAID

Laboratory of Mathematics and its Application, University Oran1 Ahmed Benbella, Algeria.

*Author to whom correspondence should be addressed.

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Abstract

In this work we developed a geometric approach to solve the problem of an isometric immersion of the Lorentzian Heisenberg space H₃ in the Euclidean space of dimension n. The Lorentzian Heisenberg space H₃ can be seen as the space ℝ³ endowed with a left Lorentzian metric, then we use a geometric approach to show that the Heisenberg group cannot be formed as a submanifold of the Euclidean space of dimension 4 see [1].

Keywords: Isometric immersionl lorentzian Heisenberg space;, weintgarten operator.

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