Discrete Laplace cycles of period four

Hans-Peter Schröcker

Open Mathematics (2012)

  • Volume: 10, Issue: 2, page 426-439
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Hans-Peter Schröcker. "Discrete Laplace cycles of period four." Open Mathematics 10.2 (2012): 426-439. <http://eudml.org/doc/269134>.

@article{Hans2012,
abstract = {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.},
author = {Hans-Peter Schröcker},
journal = {Open Mathematics},
keywords = {Discrete conjugate net; Laplace transform; Asymptotic transform; Discrete W-congruence; Discrete projective differential geometry; discrete conjugate net; asymptotic transform; discrete -congruence; discrete projective differential geometry},
language = {eng},
number = {2},
pages = {426-439},
title = {Discrete Laplace cycles of period four},
url = {http://eudml.org/doc/269134},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Hans-Peter Schröcker
TI - Discrete Laplace cycles of period four
JO - Open Mathematics
PY - 2012
VL - 10
IS - 2
SP - 426
EP - 439
AB - 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.
LA - eng
KW - Discrete conjugate net; Laplace transform; Asymptotic transform; Discrete W-congruence; Discrete projective differential geometry; discrete conjugate net; asymptotic transform; discrete -congruence; discrete projective differential geometry
UR - http://eudml.org/doc/269134
ER -

References

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