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This research investigates the conditions necessary for compact homogeneous spaces to support G-g.o. metrics.

June 19, 2026

Invariant geodesic orbit metrics on homogeneous spaces with intermediate subgroups

Key Points

This research investigates the conditions necessary for compact homogeneous spaces to support G-g.o. metrics.
Studied g.o. metrics on compact homogeneous spaces G/H with intermediate subgroup K where H ⊂ K ⊂ G.
Developed methods to establish G-g.o. metrics based on representations of K/H and G/K.
Proved that restricted metrics on K/H and G/K are g.o. metrics under specific conditions.
Found that g.o. metrics can be generated on G/H using the conditions specified.
Showed that SO(11)/(Spin(7)×SO(2)) can have non-naturally reductive g.o. metrics.
Demonstrated that g.o. metrics exist under the defined intermediate subgroup relationships.

Abstract

In this paper, we study G -g.o. metrics on compact homogeneous spaces G / H with an intermediate subgroup K such that H ⊂ K ⊂ G . In the beginning, we prove that the restricted metrics of g on K / H and G / K are both g.o. metrics under certain conditions when g is a G -g.o. metric on G / H . Then we develop several methods to determine G -g.o. metrics on G / H by the representations of K / H and G / K . As an application, we study g.o. metrics on a class of homogeneous spaces and find that SO ( 11 ) / ( Spin ( 7 ) × SO ( 2 ) ) admits non-naturally reductive g.o. metrics.

Invariant geodesic orbit metrics on homogeneous spaces with intermediate subgroups

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Abstract

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