Representations of compact Lie groups and the osculating spaces of their orbits

Abstract

Several classes of irreducible orthogonal representations of compact Lie groups that are of importance in Differential Geometry have the property that the second osculating spaces of all of their nontrivial orbits coincide with the representation space. We say that representations with this property are of class O^2. Our approach in the present paper will be to find restrictions on the class O^2 and then apply them to classify variationally complete and taut representations. The known classifications of cohomogeneity one and two orthogonal representations and more generally of polar representations will also follow easily.

arXiv commentLatex, 88 pages

References in corpus (1)

• Cycles of Bott-Samelson type for taut representations

Cited by in corpus (6)

• Homogeneity rank of real representations of compact Lie groups
• Polar orthogonal representations of real reductive algebraic groups
• Extrinsic homogeneity of parallel submanifolds
• Copolarity of isometric actions
• On parallel submanifolds of symmetric spaces
• Variationally complete actions on compact symmetric spaces