On Differential Characteristic Classes of Metrics and Connections
| Autor: | D. A. Timashev |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Pure mathematics Differential form Applied Mathematics General Mathematics 010102 general mathematics Mathematical analysis 01 natural sciences Manifold Cohomology Characteristic class Connection (mathematics) 0103 physical sciences Local coordinates Metric (mathematics) Mathematics::Differential Geometry 010307 mathematical physics 0101 mathematics Differential (mathematics) Mathematics |
| Zdroj: | Journal of Mathematical Sciences. 223:763-774 |
| ISSN: | 1573-8795 1072-3374 |
| Popis: | A differential characteristic class of a geometric quantity (e.g., Riemannian or Kahler metric, connection, etc.) on a smooth manifold is a closed differential form whose components are expressed in the components of the given geometric quantity and in their partial derivatives in local coordinates via algebraic formulas independent of the choice of coordinates, and whose cohomology class is stable under deformations of the given quantity. In this note, we present a short proof of the theorem of P. Gilkey on characteristic classes of Riemannian metrics, which is based on the method of invariant-theoretic reduction developed by P. I. Katsylo and D. A. Timashev, and generalize this result to Kahler metrics and connections. |
| Databáze: | OpenAIRE |
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