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arXiv · 1603.07956

A possible symplectic framework for Radon-type transforms

Michel Cahen·Thibaut Grouy·Simone Gutt
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Abstract

Our project is to define Radon-type transforms in symplectic geometry. The chosen framework consists of symplectic symmetric spaces whose canonical connection is of Ricci-type. They can be considered as symplectic analogues of the spaces of constant holomorphic curvature in K\"ahlerian Geometry. They are characterized amongst a class of symplectic manifolds by the existence of many totally geodesic symplectic submanifolds. We present a particular class of Radon type tranforms, associating to a smooth compactly supported function on a homogeneous manifold $M$, a function on a homogeneous space $N$ of totally geodesic submanifolds of $M$, and vice versa. We describe some spaces $M$ and $N$ in such Radon-type duality with $M$ a model of symplectic symmetric space with Ricci-type canonical connection and $N$ an orbit of totally geodesic symplectic submanifolds.

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Michel Cahen, Thibaut Grouy, Simone Gutt. 2016-03-25. A possible symplectic framework for Radon-type transforms. https://doi.org/10.1142/s0219887816410024

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