A Kähler Structure on Cartan Spaces
arXiv:1003.2518
Abstract
In this paper, we define a new metric on Cartan manifolds and obtain a Kähler structure on their cotangent bundles. We prove that on a Cartan manifold M of negative constant flag curvature, (T* M_0, G, J) has a Käahlerian structure. For Cartan manifolds of positive constant flag curvature, we show that the tube around the zero section has a Käahlerian structure. Finally by computing the Levi-Civita connection and components of curvature related to this metric, we show that there is no non- Riemannian Cartan structure such that (T* M_0, G, J) became a Einstein manifold or locally symmetric manifold.
arXiv admin note: text overlap with http://www.mathem.pub.ro/proc/bsgp-11/0ANAST02.PDF and arXiv:1202.6202 by other author
References in corpus (4)
- Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
- Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces
- Deformation Quantization of Nonholonomic Almost Kahler Models and Einstein Gravity
- Clifford-Finsler Algebroids and Nonholonomic Einstein-Dirac Structures