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Rolling Maps and Nonlinear Data

In: Handbook of Variational Methods for Nonlinear Geometric Data

Author

Listed:
  • Knut Hüper

    (Julius-Maximilians-Universität Würzburg, Institute of Mathematics)

  • Krzysztof A. Krakowski

    (Uniwersytet Kardynała Stefana Wyszyńskiego, Wydział Matematyczno-Przyrodniczy)

  • Fátima Silva Leite

    (University of Coimbra, Department of Mathematics and Institute of Systems and Robotics)

Abstract

In this chapter we study solutions to certain interpolation problems on Riemannian manifolds. Our methodology is based on rolling motions of those manifolds considered as rigid bodies, subject to holonomic as well as non-holonomic constraints. Although our approach is quite general, we focus our attention to three specific examples, namely spheres, Graßmannians and special orthogonal groups due to their importance in applications.

Suggested Citation

  • Knut Hüper & Krzysztof A. Krakowski & Fátima Silva Leite, 2020. "Rolling Maps and Nonlinear Data," Springer Books, in: Philipp Grohs & Martin Holler & Andreas Weinmann (ed.), Handbook of Variational Methods for Nonlinear Geometric Data, chapter 0, pages 577-610, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-31351-7_21
    DOI: 10.1007/978-3-030-31351-7_21
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