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Discovery Projects - Grant ID: DP140100851

Title
Discovery Projects - Grant ID: DP140100851
Funding
ARC | Discovery Projects
Contract (GA) number
DP140100851
Start Date
2014/01/01
End Date
2016/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/DP140100851

 

  • Surface theory in discrete projective differential geometry. I. A canonical frame and an integrable discrete Demoulin system

    Schief, W. K.; Szereszewski, A. (2018)
    Projects: ARC | Discovery Projects - Grant ID: DP140100851 (DP140100851)
    We present the first steps of a procedure which discretises surface theory in classical projective differential geometry in such a manner that underlying integrable structure is preserved. We propose a canonical frame in terms of which the associated projective Gauss-Weingarten and Gauss-Mainardi-Codazzi equations adopt compact forms. Based on a scaling symmetry which injects a parameter into the linear Gauss-Weingarten equations, we set down an algebraic classification scheme of discrete pro...

    Discrete projective minimal surfaces

    McCarthy, A.; Schief, W. K. (2018)
    Projects: ARC | Discovery Projects - Grant ID: DP140100851 (DP140100851)
    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 disc...
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