An example of the geometry of a 5th-order ODE: the metric on the space of conics in ${\mathbb{CP}}^2$

Maciej Dunajski; Paul Tod

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arXiv · 1801.08430

An example of the geometry of a 5th-order ODE: the metric on the space of conics in ${\mathbb{CP}}^2$

Maciej Dunajski·Paul Tod

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Abstract

As an application of the method of [4], we find the metric and connection on the space of conics in $\mathbb{CP}^2$ determined as the solution space of the ODE eqn(1). These calculations underpin the twistor construction of the Radon transform on conics in $\mathbb{CP}^2$ described in [5]. Two further examples of the method are provided.

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Maciej Dunajski, Paul Tod. 2018-01-25. An example of the geometry of a 5th-order ODE: the metric on the space of conics in ${\mathbb{CP}}^2$. https://arxiv.org/abs/1801.08430

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