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A minimal immersion of the hyperbolic plane into the neutral pseudo-hyperbolic 4-space and its characterization - MaRDI portal

A minimal immersion of the hyperbolic plane into the neutral pseudo-hyperbolic 4-space and its characterization (Q2380757)

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A minimal immersion of the hyperbolic plane into the neutral pseudo-hyperbolic 4-space and its characterization
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    A minimal immersion of the hyperbolic plane into the neutral pseudo-hyperbolic 4-space and its characterization (English)
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    12 April 2010
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    It is well known that there are no minimal surfaces of constant curvature lying fully in the hyperbolic \(4\)-space \(H^4(-1)\). In contrast, in this paper, the author discovered a minimal immersion of the hyperbolic plane \(H(-\frac13)\) of curvature \(-\frac13\) into the neutral pseudo-hyperbolic \(4\)-space \(H_2^{4}(-1)\). Moreover, he proves that, up to rigid motions of \(H_2^{4}(-1)\), this minimal immersion provides the only space-like parallel minimal surface lying fully in \(H_2^{4}(-1)\).
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    space-like surface
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    minimal surface
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    pseudo-hyperbolic space
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    Veronese surface
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