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Discrete projective minimal surfaces. (arXiv:1801.08428v1 [math.DG])
来源于:arXiv
We propose a natural discretisation scheme for classical projective minimal
surfaces. We follow the classical geometric characterisation and classification
of projective minimal surfaces and introduce at each step canonical discrete
models of the associated geometric notions and objects. Thus, we introduce
discrete analogues of classical Lie quadrics and their envelopes and classify
discrete projective minimal surfaces according to the cardinality of the class
of envelopes. This leads to discrete versions of Godeaux-Rozet, Demoulin and
Tzitzeica surfaces. The latter class of surfaces requires the introduction of
certain discrete line congruences which may also be employed in the
classification of discrete projective minimal surfaces. The classification
scheme is based on the notion of discrete surfaces which are in asymptotic
correspondence. In this context, we set down a discrete analogue of a classical
theorem which states that an envelope (of the Lie quadrics) of a surface is in
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