Jacobi relations on naturally reductive spaces
| Autor: | Tillmann Jentsch, Gregor Weingart |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Constant coefficients
Pure mathematics Geodesic Jacobi operator 010102 general mathematics 01 natural sciences Complex space Differential geometry Ordinary differential equation 0103 physical sciences Torsion (algebra) 010307 mathematical physics Geometry and Topology 0101 mathematics Algebraic number Analysis Mathematics |
| Zdroj: | Annals of Global Analysis and Geometry. 59:109-156 |
| ISSN: | 1572-9060 0232-704X |
| Popis: | Naturally reductive spaces, in general, can be seen as an adequate generalization of Riemannian symmetric spaces. Nevertheless, there are some that are closer to symmetric spaces than others. On the one hand, there is the series of Hopf fibrations over complex space forms, including the Heisenberg groups with their metrics of type H. On the other hand, there exist certain naturally reductive spaces in dimensions 6 and 7 whose torsion forms have a distinguished algebraic property. All these spaces generalize geometric or algebraic properties of three-dimensional naturally reductive spaces and have the following point in common: along every geodesic, the Jacobi operator satisfies an ordinary differential equation with constant coefficients which can be chosen independently of the given geodesic. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink