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June 2017 Trajectory-harps and Horns Applied to the Study of the Ideal Boundary of a Hadamard Kähler Manifold
Toshiaki ADACHI, Qingsong SHI
Tokyo J. Math. 40(1): 223-236 (June 2017). DOI: 10.3836/tjm/1502179224

Abstract

A trajectory-harps is made of a trajectory for a Kähler magnetic field $\mathbb{B}_{\kappa}$ and an associated variation of geodesics, and a trajectory-horn is made of a geodesic and an associated variation of trajectories. On a Hadamard Kähler manifold $M$ we study thickness and string-angles of trajectory-harps, and study tube-lengths and tube-angles of trajectory-horns. As an application of these we show that two distinct points on the compactification of $M$ with geometric ideal boundary can be joined by a trajectory for $\mathbb{B}_{\kappa}$ if the strength $|\kappa|$ is less than the upper bound of sectional curvatures of $M$.

Citation

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Toshiaki ADACHI. Qingsong SHI. "Trajectory-harps and Horns Applied to the Study of the Ideal Boundary of a Hadamard Kähler Manifold." Tokyo J. Math. 40 (1) 223 - 236, June 2017. https://doi.org/10.3836/tjm/1502179224

Information

Published: June 2017
First available in Project Euclid: 8 August 2017

zbMATH: 1373.53054
MathSciNet: MR3689987
Digital Object Identifier: 10.3836/tjm/1502179224

Subjects:
Primary: 53C22
Secondary: 53B35

Rights: Copyright © 2017 Publication Committee for the Tokyo Journal of Mathematics

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Vol.40 • No. 1 • June 2017
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