TL;DR
This paper introduces the concept of partial Jacobi manifolds within the convenient calculus framework, providing explicit examples and analyzing their characteristic distributions, thus opening new avenues for research in differential geometry.
Contribution
It defines partial Jacobi manifolds in the convenient setting and offers explicit finite and infinite-dimensional examples, advancing the understanding of their structure.
Findings
Explicit examples of partial Jacobi manifolds in finite and infinite dimensions
Analysis of the characteristic distribution associated with these structures
Identification of future research directions in the field
Abstract
The notion of partial Jacobi manifold is introduced in the convenient (-complete) framework of Fr\"olicher, Kriegl, and Michor. Explicit examples are provided in both finite and infinite dimensions, and the characteristic distribution associated with this structure is analysed. Several research directions that would merit further study are indicated.
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Taxonomy
TopicsHolomorphic and Operator Theory · Geometry and complex manifolds · Spectral Theory in Mathematical Physics