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Radon Transforms and the Rigidity of the Grassmannians (AM-156) by Hubert Goldschmidt, Jacques Gasqui

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CHAPTER IV

THE REAL GRASSMANNIANS

1. The real Grassmannians

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The involutio-179485985n of X, corresponding to the change of orientation of an m-plane of F, is an isometry of X. The group -179485785of isometries of X generated by -179485585, which is of order 2, acts freely on X and we may consider the Riemannian manifold endowed with the Riemannian metric gY induced by g. The natural ...

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