اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPolar foliations on symmetric spaces
453
0
0.0
(
0
)
تأليف
Alexander Lytchak
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
In this paper, we study polar foliations on simply connected symmetric spaces with non-negative curvature. We will prove that all such foliations are isoparametric as defined by Heintze, Liu and Olmos. We will also prove a splitting theorem which red
uces the study of such foliations to polar foliations in compact simply connected symmetric spaces. Moreover, we will show that solutions to mean curvature flow of regular leaves in such foliations are always ancient solutions. This generalizes part of the results of Liu and Terng for the mean curvature flow of isoparametric submanifolds in spheres.
We introduce a category of rigid geometries on singular spaces which are leaf spaces of foliations and are considered as leaf manifolds. We single out a special category $mathfrak F_0$ of leaf manifolds containing the orbifold category as a full subc
ategory. Objects of $mathfrak F_0$ may have non-Hausdorff topology unlike the orbifolds. The topology of some objects of $mathfrak F_0$ does not satisfy the separation axiom $T_0$. It is shown that for every ${mathcal N}in Ob(mathfrak F_0)$ a rigid geometry $zeta$ on $mathcal N$ admits a desingularization. Moreover, for every such $mathcal N$ we prove the existence and the uniqueness of a finite dimensional Lie group structure on the automorphism group $Aut(zeta)$ of the rigid geometry $zeta$ on $mathcal{N}$.
In this paper, we classify three-locally-symmetric spaces for a connected, compact and simple Lie group. Furthermore, we give the classification of invariant Einstein metrics on these spaces.
An involutive diffeomorphism $sigma$ of a connected smooth manifold $M$ is called dissecting if the complement of its fixed point set is not connected. Dissecting involutions on a complete Riemannian manifold are closely related to constructive quant
um field theory through the work of Dimock and Jaffe/Ritter on the construction of reflection positive Hilbert spaces. In this article we classify all pairs $(M,sigma)$, where $M$ is an irreducible symmetric space, not necessarily Riemannian, and $sigma$ is a dissecting involutive automorphism. In particular, we show that the only irreducible $1$-connected Riemannian symmetric spaces are $S^n$ and $H^n$ with dissecting isometric involutions whose fixed point spaces are $S^{n-1}$ and $H^{n-1}$, respectively.
We consider horofunction compactifications of symmetric spaces with respect to invariant Finsler metrics. We show that any (generalized) Satake compactification can be realized as a horofunction compactification with respect to a polyhedral Finsler metric.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
