Reflection Principles for Zero Mean Curvature Surfaces in the Simply Isotropic 3-space
Tóm tắt
Zero mean curvature surfaces in the simply isotropic 3-space
$${\mathbb {I}}^3$$
naturally appear as intermediate geometry between geometry of minimal surfaces in
$${\mathbb {E}}^3$$
and that of maximal surfaces in
$${\mathbb {L}}^3$$
. In this paper, we investigate reflection principles for zero mean curvature surfaces in
$${\mathbb {I}}^3$$
as with the above surfaces in
$${\mathbb {E}}^3$$
and
$${\mathbb {L}}^3$$
. In particular, we show a reflection principle for isotropic line segments on such zero mean curvature surfaces in
$${\mathbb {I}}^3$$
, along which the induced metrics become singular.
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