Polar actions on compact rank one symmetric spaces are taut

秩一对称空间上的极齐次叶状结构

Polar homogeneous foliations on symmetric spaces of rank one

本文分类了非紧型秩一对称空间上极齐次叶状结构在轨道等价意义下的所有情形。

Polar actions on symmetric spaces of higher rank

We show that polar actions of cohomogeneity two on simple compact Lie groups of higher rank, endowed with a biinvariant Riemannian metric, are hyperpolar. Combining this with a recent result of the second-named author, we are able to prove that polar actions induced by reductive algebraic subgroups in the isometry group of an irreducible Riemannian symmetric space of higher rank are hyperpolar. In particular, this result affirmatively settles the conjecture that polar actions on irreducible compact symmetric spaces of higher rank are hyperpolar.

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

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 representa…

Rank of ordinary webs in codimension one. An effective method

We are interested by holomorphic $d$-webs $W$ of codimension one in a complex $n$-dimensional manifold $M$. If they are ordinary, i.e. if they satisfy to some condition of genericity (whose precise definition is recalled), we proved in [CL] that their rank $ρ(W)$ is upper-bounded by a certain number $π'(n,d)\ \bigl($which, for $n\geq 3$, is stictly smaller than the Castelnuovo-Chern's bound $π(n,d)\bigr)$. In fact, denoting by $c(n,h)$ the dimension of the space of homogeneous polynomials of degree $h$ with $n$ unknowns, and by $h_0$ the integer such that $$c(n,h_0-1)<d\leq c(n,h_0),$$ $π'(n,d…

亚交换李群中秩2极化的萨德性质

Sard property for rank 2 polarizations in metabelian Lie groups

研究亚交换李群上秩2极化的异常集维数界及相关萨德性质，通过给出维数界确立终点映射萨德性质，还得到特定亚交换李群戈赫异常集维数界，推断相关极化群满足极小化萨德性质。

Polar foliations on symmetric spaces

We prove that a polar foliation of codimension at least three in an irreducible compact symmetric space is hyperpolar, unless the symmetric space has rank one. For reducible symmetric spaces of compact type, we derive decomposition results for polar foliations.