Biliotti's conjecture on polar actions on higher-rank compact symmetric spaces
Let be an irreducible compact Riemannian symmetric space of rank greater than one, and let a connected Lie group act nontrivially and polarly on . A polar action is one admitting a section meeting every orbit orthogonally, while a hyperpolar action has a flat section. Biliotti's conjecture. Every such polar action is hyperpolar. This is still an open problem for compact Lie groups of classical type.
References
Primary source
Andreas Kollross, “Duality of symmetric spaces and polar actions”, arXiv:1101.1675 (2011).
Additional references
3 papers in this index state this conjecture (2008–2011). The statement above is taken from the most recent of them; the others are arXiv:1001.3535, arXiv:0804.1677.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
No solutions have been posted yet.