Principal bundles of embeddings and nonlinear Grassmannians
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We present several principal bundles of embeddings of compact manifolds (with or without boundary) whose base manifolds are nonlinear Grassmannians. We study their infinite dimensional differential manifold structure in the Fréchet category. This study is motivated by the occurrence of such objects in the geometric Lagrangian formulation of free boundary continuum mechanics and in the study of the associated infinite dimensional dual pair structures.
KeywordsNonlinear Grassmannian Manifolds of embeddings Fréchet manifold
MSC classification (2010)46T05 58D05 58D10 58D15
This work was partially supported by a grant of the Romanian National Authority for Scientific Research, CNCS UEFISCDI, project number PN-II-ID-PCE-2011-3-0921.
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