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1999 Affine spheres: discretization via duality relations
Alexander I. Bobenko, Wolfgang K. Schief
Experiment. Math. 8(3): 261-280 (1999).

Abstract

Affine spheres with definite and indefinite Blaschke metric are discretized in a purely geometric manner. The technique is based on simple relations between affine spheres and their duals which possess natural discrete analogues. The geometry of these duality relations is discussed in detail. Cauchy problems are posed and shown to admit unique solutions. Particular discrete definite affine spheres are shown to include regular polyhedra and some of their generalizations. Connections with integrable partial difference equations and symmetric mappings are recorded.

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Alexander I. Bobenko. Wolfgang K. Schief. "Affine spheres: discretization via duality relations." Experiment. Math. 8 (3) 261 - 280, 1999.

Information

Published: 1999
First available in Project Euclid: 9 March 2003

zbMATH: 0972.53012
MathSciNet: MR1724159

Subjects:
Primary: 53A15
Secondary: 37K25 , 39A12

Rights: Copyright © 1999 A K Peters, Ltd.

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Vol.8 • No. 3 • 1999
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