RT Journal Article
T1 Transformations of quadrilateral lattices
A1 Doliwa, Adam
A1 Santin, Maria Santin
A1 Mañas Baena, Manuel Enrique
AB Motivated by the classical studies on transformations of conjugate nets, we develop the general geometric theory of transformations of their discrete analogs: the multidimensional quadrilateral lattices, i.e., lattices x:Z(N)--> R-M, N less than or equal to M, whose elementary quadrilaterals are planar. Our investigation is based on the discrete analog of the theory of the rectilinear congruences, which we also present in detail. We study, in particular, the discrete analogs of the Laplace, Combescure, Levy, radial, and fundamental transformations and their interrelations. The composition of these transformations and their permutability is also investigated from a geometric point of view. The deep connections between "transformations" and "discretizations" is also investigated for quadrilateral lattices. We finally interpret these results within the <(partial derivative)over bar> formalism.
PB American Institute of Physics
SN 0022-2488
YR 2000
FD 2000-02
LK https://hdl.handle.net/20.500.14352/59689
UL https://hdl.handle.net/20.500.14352/59689
LA eng
NO ©2000 American Institute of Physics.A.D. would like to thank A. Sym for pointing out (see also Ref. 47) the important role of the rectilinear congruences in the theory of integrable geometries (soliton surfaces). He also acknowledges partial support from KBN Grant No. 2P03 B 18509. M.M. acknowledges partial support from CICYT Proyect No. PB95-0401 and from the exchange agreement between Università La Sapienza of Rome and Universidad Complutense of Madrid
NO KBN
NO CICYT
DS Docta Complutense
RD 31 dic 2025