Nonlinear flag manifolds as coadjoint orbits-Reference-Cited by-同舟云学术

Nonlinear flag manifolds as coadjoint orbits

Published:2020-09-08 Issue:4 Volume:58 Page:385-413
ISSN:0232-704X
Container-title:Annals of Global Analysis and Geometry
language:en
Short-container-title:Ann Glob Anal Geom

Author:

Haller Stefan^ORCID,Vizman Cornelia^ORCID

Abstract

AbstractA nonlinear flag is a finite sequence of nested closed submanifolds. We study the geometry of Fréchet manifolds of nonlinear flags, in this way generalizing the nonlinear Grassmannians. As an application, we describe a class of coadjoint orbits of the group of Hamiltonian diffeomorphisms that consist of nested symplectic submanifolds, i.e., symplectic nonlinear flags.

Funder

Austrian Science Fund

Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii

Publisher

Springer Science and Business Media LLC

Subject

Geometry and Topology,Analysis

Link

https://link.springer.com/content/pdf/10.1007/s10455-020-09725-6.pdf

Reference28 articles.

1. Bauer, M., Bruveris, M., Michor, P.W.: Overview of the geometries of shape spaces and diffeomorphism groups. J. Math. Imaging Vision 50, 60–97 (2014)

2. Binz, E., Fischer, H.R.: The manifold of embeddings of a closed manifold. In: Differential Geometric Methods in Mathematical Physics (Proceedings of an International Conference Held at the Technical University of Clausthal, Clausthal-Zellerfeld, 1978). Lecture Notes in Physics, vol. 139, pp. 310–329. Springer, Berlin (1981). With an appendix by P. Michor

3. Charlier, B., Charon, N., Trouvé, A.: The fshape framework for the variability analysis of functional shapes. Found. Comput. Math. 17(2), 287–357 (2017)

4. Charon, N., Charlier, B., Trouvé, A.: Metamorphoses of functional shapes in Sobolev spaces. Found. Comput. Math. 18(6), 1535–1596 (2018)

5. Charon, N., Trouvé, A.: Functional currents: a new mathematical tool to model and analyse functional shapes. J. Math. Imaging Vision 48(3), 413–431 (2014)

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