Geometric Structures on Loop and Path Spaces

Proceedings Mathematical Sciences

Francisco Presas¹  Vicente Muñoz² 

[1] Instituto de Ciencias Matemáticas CSIC-UAM-UCM-UCM, Serrano bis, 00 Madrid, Spain$$;Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad Complutense de Madrid, 00 Madrid, Spain$$

关键词: Loop space;    symplectic structures;    contact structures.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

The loop space associated to a Riemannian manifold admits a quasi-symplectic structure (that is, a closed 2-form which is non-degenerate up to a finite-dimensional kernel). We show how to construct a compatible almost-complex structure. Finally conditions to have contact structures on loop spaces are studied.

【 授权许可】

Unknown