6 papers
The Frolicher-Nijenhuis Calculus in Synthetic Differential Geometry
Hirokazu Nishimura
Just as the Jacobi identity of vector fields is a natural consequence of the general Jacobi identity of microcubes in synthetic differential geometry, it is to be shown in this pap…
A Functorial Approach to the Infinitesimal Theory of Groupoids
Hirokazu Nishimura
Lie algebroids are by no means natural as an infinitesimal counterpart of groupoids. In this paper we propose a functorial construction called Nishimura algebroids for an infinites…
Curvature in Synthetic Differential Geometry of Groupoids
Hirokazu Nishimura
We study the fundamental properties of curvature in groupoids within the framework of synthetic differential geometry. As is usual in synthetic differential geometry, its combinato…
The Lie algebra of the group of bisections
Hirokazu Nishimura
Groupoids provide a more appropriate framework for differential geometry than principal bundles. Synthetic differential geometry is the avant-garde branch of differential geometry,…
Another coboundary operator for differential forms with values in the Lie algebra bundle of a group bundle
Hirokazu Nishimura
Kock [Bull. Austral. Math. Soc., 25 (1982), 357-386] has considered differential forms with values in a group in a context where neighborhood relations are available. By doing so,…
The affine bundle theorem in synthetic differential geometry of jet bundles
Hirokazu Nishimura
In our [Higher-order preconnections in synthetic differential geometry of jet bundles, Beiträge zur Algebra und Geometrie, 45 (2004), 677-696] we have established the affine bundle…