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

作者：Chen Bang Yen^*

来源：Archiv der Mathematik, 2010, 94(3): 291-299.

DOI：10.1007/s00013-009-0094-4

• Space-like surface
• Minimal surface
• Pseudo-hyperbolic space
• Veronese surface

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 article we discover a minimal immersion of the hyperbolic plane H-2(-1/3) of curvature -1/3 into the neutral pseudo-hyperbolic 4-space H-2(4)(-1). Moreover, we prove 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).

• 出版日期2010-3