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On the inverse problem of determining a connection on a vector bundle
Published/Copyright:
September 7, 2013
Abstract
- We consider the problem of determining a connection on a vector bundle over a compact Riemannian manifold with boundary from the known parallel transport between boundary points along geodesics. The main result is the local uniqueness theorem: if two connections ∇' and ∇'' are C-close to a given connection ∇ whose curvature tensor is sufficiently small, then the coincidence of parallel transports with respect to ∇' and ∇'' implies the existence of an automorphism of the bundle which is identical on the boundary and transforms ∇' to ∇'' . A linearized version of the problem is also considered.
Published Online: 2013-09-07
Published in Print: 2000-02
© 2013 by Walter de Gruyter GmbH & Co.
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- On the inverse problem of determining a connection on a vector bundle
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Articles in the same Issue
- CONTENTS
- Identifiability of distributed parameters for high-order quasi-linear differential equations
- Theory of ground-penetrating radars III
- Stability and convergence of the wavelet-Galerkin method for the sideways heat equation
- On the inverse problem of determining a connection on a vector bundle
- Inverse problems for differential equations with singularities lying inside the interval
