紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2025, 62(2), p. 185-197

PSEUDO-RIEMANNIAN GEODESIC ORBIT METRICS ON CERTAIN COMPACT HOMOGENEOUS SPACES

Departments of Mathematics, The University of Osaka and Osaka Metropolitan University

英語

text

2025-04

A pseudo-Riemannian metric is called geodesic orbit if its geodesics are the orbits of oneparameter subgroups of the group of isometries. In this paper, we study pseudo-Riemannian geodesic orbit metrics on compact homogeneous spaces. First we obtain a sufficient and necessary condition for a pseudo-Riemannian metric to be geodesic orbit. Then we show that every Tamaru’s homogeneous space admits a two-parameter family of pseudo-Riemannian geodesic orbit metrics. Finally, we obtain a complete description of pseudo-Riemannian geodesic orbit metrics on spheres. In particular, we prove that a Sp(n+1)-invariant pseudo-Riemannian geodesic orbit metric on S⁴ⁿ⁺³ = Sp(n + 1)/Sp(n) must be Sp(n + 1)Sp(1)-invariant.

10.18910/101124

101124

PSEUDO-RIEMANNIAN GEODESIC ORBIT METRICS ON CERTAIN COMPACT HOMOGENEOUS SPACES

Departments of Mathematics, The University of Osaka and Osaka Metropolitan University

英語

2025-04

Osaka Journal of Mathematics

62

2

185

197

https://hdl.handle.net/11094/101124

10.18910/101124

https://doi.org/10.18910/101124