Geodesic
Minimal linear Morse functions on the orbits in Lie algebras
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2015), pp. 9-16

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A theorem stating that all Morse height functions are perfect on regular orbits of the adjoint action of compact semisimple Lie groups is proved. In the case of arbitrary linear representation of a compact Lie group we prove that all height functions are Bott functions on orbits of representation. The case of $\mathrm{SO}_{4}$ is studied in more detail. 
@article{VMUMM_2015_2_a1,
     author = {V. A. Shmarov},
     title = {Minimal linear {Morse} functions on the orbits in {Lie} algebras},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {9--16},
     publisher = {mathdoc},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_2_a1/}
}
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V. A. Shmarov. Minimal linear Morse functions on the orbits in Lie algebras. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2015), pp. 9-16. http://geodesic.mathdoc.fr/item/VMUMM_2015_2_a1/