Almost Kaehler geometry of adjoint orbits of semisimple Lie groups
Differential Geometry
2018-11-27 v2 Symplectic Geometry
Abstract
We study the almost Kaehler geometry of adjoint orbits of non-compact real semisimple Lie groups endowed with the Kirillov-Kostant-Souriau symplectic form and a canonically defined almost complex structure. We give explicit formulas for the Chern-Ricci form, the Hermitian scalar curvature and the Nijenhuis tensor in terms of root data. We also discuss when the Chern-Ricci form is a multiple of the symplectic form, and when compact quotients of these orbits are of Kaehler type.
Keywords
Cite
@article{arxiv.1811.06958,
title = {Almost Kaehler geometry of adjoint orbits of semisimple Lie groups},
author = {Alberto Della Vedova and Alice Gatti},
journal= {arXiv preprint arXiv:1811.06958},
year = {2018}
}
Comments
42 pages. Exposition improved. Appendix enhanced with more tables and more data. Many typos fixed