Isometric foldings
Isometric foldings
An isometric folding from a Riemannian manifold M to another N is a map which sends piecewise geodesic segments on M to piecewise geodesic segments on N of the same length. The set (ImM, N) of all isometric foldings from M to N has, as a subset of all continuous functions from M to N, a natural C0 topology. The main purpose of this Thesis is to obtain descriptions of the topological spaces of all isometric self-foldings of the Riemannian 2-sphere S2, of the Euclidean plane Re2 and of the hyperbolic plane cal H2, given in Chapters 3, 4 and 5 respectively. In Chapter 1 we review the general theory of isometric foldings of Riemannian manifolds. In Chapter 2 we study a subspace of (Im M, N) formed by all isometric foldings of finite type, that is by all isometric foldings f whose set of singularities, (points where f fails to be differentiable), partitions M into a finite number of regions on which f is an isometric immersion. Finally in Chapter 6 we give a brief outline of the main results and some open problems are proposed.
University of Southampton
Reis D'Azevedo Bredo, Ana Maria
1989
Reis D'Azevedo Bredo, Ana Maria
Reis D'Azevedo Bredo, Ana Maria
(1989)
Isometric foldings.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
An isometric folding from a Riemannian manifold M to another N is a map which sends piecewise geodesic segments on M to piecewise geodesic segments on N of the same length. The set (ImM, N) of all isometric foldings from M to N has, as a subset of all continuous functions from M to N, a natural C0 topology. The main purpose of this Thesis is to obtain descriptions of the topological spaces of all isometric self-foldings of the Riemannian 2-sphere S2, of the Euclidean plane Re2 and of the hyperbolic plane cal H2, given in Chapters 3, 4 and 5 respectively. In Chapter 1 we review the general theory of isometric foldings of Riemannian manifolds. In Chapter 2 we study a subspace of (Im M, N) formed by all isometric foldings of finite type, that is by all isometric foldings f whose set of singularities, (points where f fails to be differentiable), partitions M into a finite number of regions on which f is an isometric immersion. Finally in Chapter 6 we give a brief outline of the main results and some open problems are proposed.
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Published date: 1989
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Local EPrints ID: 461185
URI: http://eprints.soton.ac.uk/id/eprint/461185
PURE UUID: 4ebe5d33-f9b7-4051-acb8-7c3e4aecdd8f
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Date deposited: 04 Jul 2022 18:38
Last modified: 04 Jul 2022 18:38
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Author:
Ana Maria Reis D'Azevedo Bredo
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