What is it about?
This paper contributes to the foundation of various Hofer-like topologies: Various extensions of Hofer’s metric, and some related results.
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Why is it important?
The Hofer geometry deals with paths in the kernel of the flux homomorphism. In general not all Symplectic paths are in this kernel: it seems natural to investigate whether the flux homomorphism is an obstacle to the extension of Hofer geometry to the identity component in the group of symplectomorphisms of a closed Symplectic manifold. The results of this paper show that one can define and study various extensions of Hofer’s geometry via splitting of closed $1-$forms on any closed Symplectic manifold.
Perspectives
Description of geodesics in Hofer-like geometry
Stéphane Tchuiaga
University of Buea
Read the Original
This page is a summary of: On symplectic dynamics, Differential Geometry and its Applications, December 2018, Elsevier,
DOI: 10.1016/j.difgeo.2018.09.003.
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