The Hilbert-Schmidt Lagrangian Grassmannian in infinite dimension

JOURNAL OF GEOMETRY AND PHYSICS

卷:99

Review

Lopez Galvan, Manuel¹ 

[1] Univ Nacl Gen Sarmiento, Inst Ciencias, Buenos Aires, DF, Argentina

关键词: Homogeneous space;    Riemannian metrics;    Geodesics;    Banach-Lie groups;    Lagrangian Grassmannian;   

DOI  :  10.1016/j.geomphys.2015.10.005

来源: Elsevier

【 摘 要 】

In this paper we study the action of the symplectic operators which are a perturbation of the identity by a Hilbert-Schmidt operator in the Lagrangian Grassmannian manifold. We prove several geometric properties using the quotient norm in the tangent spaces. We determinate the geodesic curves of this structure and we study the completeness of the corresponding geodesic distance. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free