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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Accordingly, this geometric structure converts to a holonomy invariant foliated cocycle on the tangent space, which is totally adapted to the Helmholtz conditions.
📌 3 Key Takeaways
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Objective & Hypothesis:This paper is dedicated to exhaustive structural analysis of the holonomy invariant foliated cocycles on the tangent bundle of an arbitrary $(m+n)$-dimensional manifold.
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Key Findings & Data:For this purpose, by applying Spencer theory of formal integrability, sufficient conditions for the metric associated with the semispray $S$ are determined to extend to a transverse metric for the lifted foliated cocycle on $TM$.
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Conclusion & Impact:Accordingly, this geometric structure converts to a holonomy invariant foliated cocycle on the tangent space, which is totally adapted to the Helmholtz conditions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Foliated cocycle · holonomy group · metrizability
Abstract
This paper is dedicated to exhaustive structural analysis of the holonomy invariant foliated cocycles on the tangent bundle of an arbitrary $(m+n)$-dimensional manifold. For this purpose, by applying Spencer theory of formal integrability, sufficient conditions for the metric associated with the semispray $S$ are determined to extend to a transverse metric for the lifted foliated cocycle on $TM$. Accordingly, this geometric structure converts to a holonomy invariant foliated cocycle on the tangent space, which is totally adapted to the Helmholtz conditions.
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Cite This Article
AHANGARI, F. (2019). Construction of the holonomy invariant foliated cocycles on the tangent bundle via formal integrability. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 81–102. https://ajindex.com/articles/212746