Díaz Ramos, José CarlosDomínguez Vázquez, MiguelKollross, Andreas2024-10-042024-10-042018Díaz-Ramos, J.C., Domínguez-Vázquez, M. & Kollross, A. On homogeneous manifolds whose isotropy actions are polar. manuscripta math. 161, 15–34 (2020)http://hdl.handle.net/10347/35013This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00229-018-1077-1We 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.engjournal article10.1007/s00229-018-1077-1open access