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

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.

arXiv comment14 pages; a new section with further examples of the method has been added. This version to appear in Differential Geometry and its Applications

References in corpus (1)

• On types of non-integrable geometries