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<p>We study geodesic orbit Riemannian manifolds, namely manifolds where all geodesics are orbits of one - parameter groups of isometries. Any connected such manifold is homogeneous, while the structure and existence of geodesic orbit metrics on a homogeneous space <i>G</i>/<i>H</i> largely depends on the embedding of the stabilizer subgroup <i>H</i> in <i>G</i>. In this article, we study and characterize the geodesic orbit metrics in the extensive class of spaces <i>G</i>/<i>H</i> with <i>G</i> compact and <i>H</i> a semisimple regular subgroup of <i>G</i> (in the sense that the Lie algebra of <i>H</i> is normalized by a Cartan subalgebra of the Lie algebra of <i>G</i>). This work is a contribution to the ongoing study of compact geodesic orbit manifolds, focusing on those with semisimple stabilizer.</p>

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Compact geodesic orbit manifolds with regular stabilizer

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • Nikolaos Panagiotis Souris

摘要

We study geodesic orbit Riemannian manifolds, namely manifolds where all geodesics are orbits of one - parameter groups of isometries. Any connected such manifold is homogeneous, while the structure and existence of geodesic orbit metrics on a homogeneous space G/H largely depends on the embedding of the stabilizer subgroup H in G. In this article, we study and characterize the geodesic orbit metrics in the extensive class of spaces G/H with G compact and H a semisimple regular subgroup of G (in the sense that the Lie algebra of H is normalized by a Cartan subalgebra of the Lie algebra of G). This work is a contribution to the ongoing study of compact geodesic orbit manifolds, focusing on those with semisimple stabilizer.