Abstract: A pseudo-Riemannian manifold \((M,g)\) is called a geodesic orbit manifold if any geodesic \(\gamma\) of \(M\) is an orbit of a \(1\)-parameter subgroup of the full isometry group of \((M,g)\). This terminology in the case of Riemannian manifolds was introduced in 1991 by O. Kowalski and L. Vanhecke, who initiated a systematic study of spaces \((M=G/H,g)\), where \(G\) is an isometry group and \(H\) is an isotropy subgroup. It should be noted that symmetric spaces, weakly symmetric spaces, naturally reductive homogeneous spaces, normal homogeneous spaces, generalized normal homogeneous spaces (but not only) are subclasses of geodesic orbit pseudo-Riemannian spaces. In this paper, we present examples of geodesic orbit pseudo-Riemannian manifolds. The examples are special \(15\)-dimensional pseudo \(H\)-type Lie groups, i.e., \(2\)-step nilpotent Lie groups of Heisenberg type equipped with a left invariant pseudo-Riemannian metric. To construct the corresponding examples, results on the structure of the Lie groups under consideration were used.
For citation: Markina, I. G., Nikonorov, Yu. G. and Furutani, K. On Examples of Geodesic Orbit Pseudo-Riemannian Manifolds, Vladikavkaz Math. J., 2026, vol. 28, no. 1, pp. 108-121. DOI 10.46698/i4125-5722-6924-j
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