34 citations · 127 across the 38 of their papers we have counts for
6 papers · 1 filter
Square-densities, and volume forms
Anders Kock
Heron's formula from antiquity, for the area of a triangle, is used to relate volume form and infinitesimal square-volume of certain infinitesimal simplices in a Riemannian manifol…
Integration of 1-forms and connections
Anders Kock
We give a combinatorial/geometric argument of the classical result that an affine connection, which is both torsion free and curvature free, is locally an affine space.
Huygens' principle - a synthetic account
Anders Kock
We present an axiomatic/synthetic account of the Huygens Principle of wave fronts. The primitive notions are "touching", and (a weak notion of ) metric. The paper simplifies some o…
New methods for old spaces: synthetic differential geometry
Anders Kock
Survey talk on certain aspects of the subject, stressing the neighbor relation as a basic notion in differential geometry.
A geometric theory of harmonic and semi-conformal maps
Anders Kock
We describe for any Riemannian manifold a certain infinitesimal neighbourhood of the diagonal. Semi-conformal maps are analyzed as those that preserve such neighbourhoods; harmonic…
First neighbourhood of the diagonal, and geometric distributions
Anders Kock
We describe the geometric notion of distribution in synthetic terms, utilizing the notion of "first neighbourhood of the diagonal" from algebraic geometry. We characterize involuti…