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Journals / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 1

Construction of the holonomy invariant foliated cocycles on the tangent bundle via formal integrability

Fatemeh AHANGARI
Pages
81–102
Publication Date
2022-11-04
DOI
—
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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 invariantfoliated cocycle on the tangent space, which is totally adapted to the Helmholtz conditions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper is dedicated to exhaustive structural analysis of the holonomy invariant foliated cocycles on thetangent bundle of an arbitrary (m + n) -dimensional manifold.
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Key Findings & Data:For this purpose, by applying Spencer theory of formalintegrability, sufficient conditions for the metric associated with the semispray S are determined to extend to a transversemetric for the lifted foliated cocycle on TM.
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Conclusion & Impact:Accordingly, this geometric structure converts to a holonomy invariantfoliated cocycle on the tangent space, which is totally adapted to the Helmholtz conditions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

This paper is dedicated to exhaustive structural analysis of the holonomy invariant foliated cocycles on thetangent bundle of an arbitrary (m + n) -dimensional manifold. For this purpose, by applying Spencer theory of formalintegrability, sufficient conditions for the metric associated with the semispray S are determined to extend to a transversemetric for the lifted foliated cocycle on TM. Accordingly, this geometric structure converts to a holonomy invariantfoliated cocycle on the tangent space, which is totally adapted to the Helmholtz conditions.

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Cite This Article

AHANGARI, F. (2022). 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/607729

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