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THE NORMAL DUAL CONGRUENCES AND THE DUAL BIANCHI LATTICE

Published online by Cambridge University Press:  14 July 2005

ADAM DOLIWA
Affiliation:
Wydział Matematyki i Informatyki, Uniwersytet Warmińsko–Mazurski w Olsztynie, ul. Żołnierska 14A, 10-561 Olsztyn, Poland e-mail: [email protected]
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Abstract

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The main goal of the paper is to find the discrete analogue of the Bianchi system in spaces of arbitrary dimension together with its geometric interpretation. We show that the proper geometric framework for such generalization is the language of dual quadrilateral lattices and of dual congruences. After introducing the notion of the dual Koenigs lattice in a projective space of arbitrary dimension, we define the discrete dual congruences and we present, as an important example, the normal dual discrete congruences. Finally, we introduce the dual Bianchi lattice as a dual Koenigs lattice allowing for a conjugate normal dual congruence, and we find its characterization in terms of a system of integrable difference equations.

Keywords

Type
Research Article
Copyright
2005 Glasgow Mathematical Journal Trust