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arXiv · 1003.2518

A Kähler Structure on Cartan Spaces

E. Peyghan·A. Tayebi
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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.

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E. Peyghan, A. Tayebi. 2010-03-12. A Kähler Structure on Cartan Spaces. https://arxiv.org/abs/1003.2518

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