A Remark on Chern-Weil Theory
We show that Chern-Weil theory for tensor bundles over manifolds is a consequence of the existence of natural closed differential forms on total spaces of torsion free connections on frame bundles.
math.DG↗
arXiv subjects
P. I. Katsylo
Publications and source records attributed to P. I. Katsylo.
Projective Invariants of Riemannian Metrics
It is understood now that all projective (and conformal) invariants of Riemannian metrics can be found by a transparent construction based on representation theory. So this article with a partial and quite cumbersome construction of projective invariants become obsolete.
math.DG↗
On Curvatures of Sections of Tensor Bundles
We consider natural differential operations acting on sections of tensor vector bundles. Arrising problems can be reformulated as invariant theoretical problems (the IT-reduction). We give examples of usage of the IT-reduction. In particular, on a manifold with a connection and a Poisson structure we construct the canonical quantization.
math.DG↗