Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1705-19
Keywords
Foliated cocycle, holonomy group, metrizability, formal integrability, transverse metric
First Page
81
Last Page
102
Recommended Citation
AHANGARI, FATEMEH
(2019)
"Construction of the holonomy invariantfoliated cocycles on the tangent bundle via formal integrability,"
Turkish Journal of Mathematics: Vol. 43:
No.
1, Article 7.
https://doi.org/10.3906/mat-1705-19
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss1/7
