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The Ribaucour transformation for flat Lagrangian submanifolds

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Abstract

We study the Ribaucour transformation for flat Lagrangian submanifolds in complex flat space and complex projective space. As a consequence, we obtain a process to generate a new family of such submanifolds from a given one. Analytically, this provides a method to construct new solutions of the corresponding systems of PDEs from a given one. We also show that such transformation always comes with a permutability formula.

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Authors and Affiliations

  1. Institute de Matematica Pura e Aplicada, IMPA, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil

    Marcos Dajczer

  2. Universidade Federal de Uberlândia, 38400-089, Uberlândia, Brazil

    Ruy Tojeiro

Authors
  1. Marcos Dajczer
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  2. Ruy Tojeiro
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Correspondence to Marcos Dajczer.

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Dajczer, M., Tojeiro, R. The Ribaucour transformation for flat Lagrangian submanifolds. J Geom Anal 10, 269–280 (2000). https://doi.org/10.1007/BF02921825

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  • DOI: https://doi.org/10.1007/BF02921825

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