A Cauchy problem for minimal spacelike surfaces in $\mathbb{R}^4_2$

Alexandre Lymberopoulos; Antonio de Padua Franco Filho; Anuar Enrique Paternina Montalvo

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arXiv · 1905.08629

A Cauchy problem for minimal spacelike surfaces in $\mathbb{R}^4_2$

Alexandre Lymberopoulos·Antonio de Padua Franco Filho·Anuar Enrique Paternina Montalvo

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Abstract

We give a definition of isoclinic parametric surfaces in $\mathbb{R}^4_2$ and prove that such an isoclinic conformal immersion comes from two holomorphic functions. A Cauchy problem was proposed and solved, namely: construct an isoclinic and minimal positive (negative) spacelike surface in $\mathbb{R}^4_2$, containing a given positive (negative) real analytic curve. At last, we study the important and well-known Bj\"orling problem, providing some examples was given in the last section.

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Alexandre Lymberopoulos, Antonio de Padua Franco Filho, Anuar Enrique Paternina Montalvo. 2019-05-21. A Cauchy problem for minimal spacelike surfaces in $\mathbb{R}^4_2$. https://arxiv.org/abs/1905.08629

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