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Please use this identifier to cite or link to this item: http://hdl.handle.net/10481/37916

Title: Ribaucour type Transformations for the Hessian One Equation
Authors: Martínez-López, Antonio
Milán López, Francisco
Tenenblat, Keti
Issue Date: 2015
Abstract: We extend the classical theory of Ribaucour transformations to the family of improper affine maps and use it to obtain new solutions of the Hessian one equation. We prove that such transformations produce complete, embedded ends of parabolic type and curves of singularities which generically are cuspidal edges. Moreover, we show that these ends and curves of singularities do no intersect. We apply Ribaucour transformations to some helicoidal improper affine maps providing new 3-parameter families with an interesting geometry and a good behavior at infinity. In particular, we construct improper affine maps, periodic in one variable, with any even number of complete embedded ends.
Sponsorship: Ministerio de Educación Grants No: MTM2013-43970-P, No: PHB2010-0109, Junta de Anadalucía Grants No. FQM325, N0. P06-FQM-01642. Ministério de Ciência e Tecnologia, CNPq Proc. No. 303774/2009-6. Ministério de Educação, CAPES/DGU Proc. No. 23038010833/2010-37.
Publisher: Elsevier
Keywords: Ribaucour transformations
Improper affine spheres
Hessian one equation
URI: http://hdl.handle.net/10481/37916
ISSN: 0362-546X
Rights : Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License
Citation: Martínez-López, A.; Milán López, F.; Tenenblat, K. Ribaucour type Transformations for the Hessian One Equation. Nonlinear Analysis: Theory, Methods and Applications, 112: 147–155 (2015). [http://hdl.handle.net/10481/37916]
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