Discrete Laplace Cycles of Period Four

Details Discrete Laplace Cycles of Period Four Discrete Laplace Cycles of Period Four

2011-04-19

arxiv.org/abs/1104.3689v1

Central European J. Mathematics, 10(2):426-439, 2012

Mathematics

Differential Geometry

Scientific paper

10.2478/s11533-011-0132-x

We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of corresponding points form a discrete W-congruence. We derive some properties of discrete Laplace cycles of period four and describe two explicit methods for their construction.

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