Corrigenda to: "Synthetic differential geometry of jet bundles''

Holonomicity in Synthetic Differential Geometry of Jet Bundles

In the repetitive approach to the theory of jet bundles there are three methods of repetition, which yield non-holonomic, semi-holonomic, and holonomic jet bundles respectively. However the classical approach to holonomic jet bundles failed to be truly repetitive, for it must resort to such a non-repetitive coordinatedependent construction as Taylor expansion. The principal objective in this pa...

Higher-Order Preconnections in Synthetic Differential Geometry of Jet Bundles

In our previous papers (Nishimura [2001 and 2003]) we dealt with jet bundles from a synthetic perch by regarding a 1-jet as something like a pinpointed (nonlinear) connection (called a preconnection) and then looking on higherorder jets as repeated 1-jets. In this paper we generalize our notion of preconnection to higher orders, which enables us to develop a non-repetitive but still synthetic a...

The Affine Bundle Theorem in Synthetic Differential Geometry of Jet Bundles

In this paper we will establish the affine bundle theorem in our synthetic approach to jet bundles in terms of infinitesimal spaces Dn’s. We will then compare these affine bundles with the corresponding ones constructed in our previous synthetic approach to jet bundles in terms of infinitesimal spacesD’s both in the general microlinear setting and in the finite-dimensional setting.

Finsler Geometry of Holomorphic Jet Bundles

Introduction 107 1. Holomorphic Jet Bundles 113 2. Chern Classes and Cohomology Groups: The Case of Curves 120 3. Computation of Chern Classes: The Case of Surfaces 139 4. Finsler Geometry of Projectivized Vector Bundles 148 5. Weighted Projective Spaces and Projectivized Jet Bundles 153 6. The Lemma of Logarithmic Derivatives and the Schwarz Lemma 164 7. Surfaces of General Type 173 Acknowledg...

Differential Geometry of Complex Vector Bundles