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GEODESIC ORBIT METRICS IN COMPACT HOMOGENEOUS MANIFOLDS WITH EQUIVALENT ISOTROPY SUBMODULES

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Abstract

A geodesic orbit manifold (GO manifold) is a Riemannian manifold (M, g) with the property that any geodesic in M is an orbit of a one-parameter subgroup of a group G of isometries of (M, g). The metric g is then called a G-GO metric in M. For an arbitrary compact homogeneous manifold M = G/H, we simplify the general problem of determining the G-GO metrics in M. In particular, if the isotropy representation of H induces equivalent irreducible submodules in the tangent space of M, we obtain algebraic conditions, under which, any G-GO metric in M admits a reduced form. As an application we determine the U(n)-GO metrics in the complex Stiefel manifolds V k ℂ n.

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  1. Department of Mathematics, University of Patras, University Campus, 26504, Rio, Greece

    NIKOLAOS PANAGIOTIS SOURIS

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  1. NIKOLAOS PANAGIOTIS SOURIS
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SOURIS, N. GEODESIC ORBIT METRICS IN COMPACT HOMOGENEOUS MANIFOLDS WITH EQUIVALENT ISOTROPY SUBMODULES. Transformation Groups 23, 1149–1165 (2018). https://doi.org/10.1007/s00031-017-9464-3

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