雅可比方程与多共轭点流形

Mathematical Proceedings of the Royal Irish Academy Pub Date : 1900-01-01 DOI:10.3318/PRIA.2013.113.03

J. Burns, Eoghan J. Staunton, D. Wraith

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引用次数: 1

摘要

研究了沿测地线的多个共轭点的现象。在第一个例子中，我们在雅可比方程的背景下研究共轭点，雅可比方程是一个二阶常微分方程，它精确地捕获了曲面上共轭点的几何形状。然后我们构造几何例子，在高维中表现出类似的性质。

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ON THE JACOBI EQUATION AND MANIFOLDS WITH MULTIPLE CONJUGATE POINTS

We investigate the phenomenon of multiple conjugate points along a geodesic. In the first instance, we investigate conjugate points in the context of the Jacobi equation, a second order ordinary differential equation, which captures precisely the geometry of conjugate points on surfaces. We then construct geometric examples which exhibit similar properties in higher dimensions.

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Mathematical Proceedings of the Royal Irish Academy

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