RESEARCH ON THE POISSON GEOMETRY AND THE RELATED GEOMETRIES

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One of the main geometric feature of a Poisson manifold is that its cotangent bundle carries a structure of a Lie algebroid. If a Lie algebroid comes from the normal bundle of the unit space of a Lie groupoid, it is called integrable. All the Lie algebroids are not integrable. Motivated by such integrability problem, we studied the powerful integrability theory (which is the theory of exterior differential systems), along with many geometric applications. As a result, we have acquired fundamental techniques to solve various integrability problems.