We study the almost Kähler 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 Kähler type.

Della Vedova, A., & Gatti, A. (2022). Almost Kähler geometry of adjoint orbits of semisimple Lie groups. MATHEMATISCHE ZEITSCHRIFT, 301(3), 3141-3183 [10.1007/s00209-022-02995-9].

Almost Kähler geometry of adjoint orbits of semisimple Lie groups

Della Vedova, A;
2022

Abstract

We study the almost Kähler 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 Kähler type.
Articolo in rivista - Articolo scientifico
Scientifica
(co)adjoint orbits; Canonical almost Kähler metrics; Homogeneous manifolds; Special metrics;
English
Della Vedova, A., & Gatti, A. (2022). Almost Kähler geometry of adjoint orbits of semisimple Lie groups. MATHEMATISCHE ZEITSCHRIFT, 301(3), 3141-3183 [10.1007/s00209-022-02995-9].
Della Vedova, A; Gatti, A
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/385726
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