A K\"ahler Structure on Cartan Spaces
Mathematical Physics
2012-10-20 v1 math.MP
Abstract
In this paper, we define a new metric on Cartan manifolds and obtain a K\"ahler 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 K\"aahlerian structure. For Cartan manifolds of positive constant flag curvature, we show that the tube around the zero section has a K\"aahlerian 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.
Cite
@article{arxiv.1003.2518,
title = {A K\"ahler Structure on Cartan Spaces},
author = {E. Peyghan and A. Tayebi},
journal= {arXiv preprint arXiv:1003.2518},
year = {2012}
}
Comments
arXiv admin note: text overlap with http://www.mathem.pub.ro/proc/bsgp-11/0ANAST02.PDF and arXiv:1202.6202 by other author