Axiomatic differential geometry II-1 - vector fields

Geometry II - Discrete Differential Geometry

Notes on Axiomatic Geometry

Axiomatic Systems for Geometry∗

An axiomatic system contains a set of primitives and axioms. The primitives are Adaptation to the current course is in the margins. object names, but the objects they name are left undefined. This is why the primitives are also called undefined terms. The axioms are sentences that make assertions about the primitives. Such assertions are not provided with any justification, they are neither tru...

Differential Geometry of Complex Vector Bundles

Geometry of Four-vector Fields on Quaternionic Flag Manifolds

The purpose of this paper is to describe certain natural 4-vector fields on quaternionic flag manifolds, which geometrically determines the Bruhat cell decomposition. This structure naturally descends from the symplectic group, where it is related to the dressing action given by the Iwasawa decomposition of the general linear group over the quaternions.