Focal radii of orbits

ABSTRACT

We show that every effective action of a compact Lie group K on a unit sphere $S^n$ admits an explicit orbit whose principal curvatures are bounded from above by $4\sqrt{14}$.

KEYWORDS:

• Compact Lie group
• focal radius
• focal point
• orbit

AMS CLASSIFICATIONS:

• 57S15
• 22E46
• 53B25

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Claudio Gorodski has been partially supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) grant [grant number 303038/2013-6] and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) project [grant number 2011/21362-2]. Artur B. Saturnino has been supported by the CNPq scholarship [grant number 154010/2015-4].