We show that simply connected Riemannian homogeneous spaces of compact semisimple Lie groups with polar isotropy actions are symmetric, generalizing results of Fabio Podestà and the third named author. Without assuming compactness, we give a classification of Riemannian homogeneous spaces of semisimple Lie groups whose linear isotropy representations are polar. We show for various such spaces that they do not have polar isotropy actions. Moreover, we prove that Heisenberg groups and non-symmetric Damek--Ricci spaces have non-polar isotropy actions.
%0 Journal Article
%1 Díaz-Ramos2020
%A Díaz-Ramos, José Carlos
%A Domínguez-Vázquez, Miguel
%A Kollross, Andreas
%D 2020
%J manuscripta mathematica
%K myown from:kollross
%N 1
%P 15--34
%R 10.1007/s00229-018-1077-1
%T On homogeneous manifolds whose isotropy actions are polar
%U https://doi.org/10.1007/s00229-018-1077-1
%V 161
%X We show that simply connected Riemannian homogeneous spaces of compact semisimple Lie groups with polar isotropy actions are symmetric, generalizing results of Fabio Podestà and the third named author. Without assuming compactness, we give a classification of Riemannian homogeneous spaces of semisimple Lie groups whose linear isotropy representations are polar. We show for various such spaces that they do not have polar isotropy actions. Moreover, we prove that Heisenberg groups and non-symmetric Damek--Ricci spaces have non-polar isotropy actions.
@article{Díaz-Ramos2020,
abstract = {We show that simply connected Riemannian homogeneous spaces of compact semisimple Lie groups with polar isotropy actions are symmetric, generalizing results of Fabio Podest{\`a} and the third named author. Without assuming compactness, we give a classification of Riemannian homogeneous spaces of semisimple Lie groups whose linear isotropy representations are polar. We show for various such spaces that they do not have polar isotropy actions. Moreover, we prove that Heisenberg groups and non-symmetric Damek--Ricci spaces have non-polar isotropy actions.},
added-at = {2021-07-07T17:07:52.000+0200},
author = {D{\'i}az-Ramos, Jos{\'e} Carlos and Dom{\'i}nguez-V{\'a}zquez, Miguel and Kollross, Andreas},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/25e1f89ba099ffa446ab266a745c2fd9f/mathematik},
day = 01,
doi = {10.1007/s00229-018-1077-1},
interhash = {ea95a92bf14e7ac53b064ecf2baf70f7},
intrahash = {5e1f89ba099ffa446ab266a745c2fd9f},
issn = {1432-1785},
journal = {manuscripta mathematica},
keywords = {myown from:kollross},
month = jan,
number = 1,
pages = {15--34},
timestamp = {2021-07-07T15:07:52.000+0200},
title = {On homogeneous manifolds whose isotropy actions are polar},
url = {https://doi.org/10.1007/s00229-018-1077-1},
volume = 161,
year = 2020
}
