Abstract.
We study the metric geometry of homogeneous reductive spaces of the unitary group of a finite von Neumann algebra with a non complete Riemannian metric. The main result gives an abstract sufficient condition in order that the geodesics of the Levi-Civita connection are locally minimal. Then, we show how this result applies to several examples.
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Chiumiento, E. Local Minimal Curves in Homogeneous Reductive Spaces of the Unitary Group of a Finite von Neumann Algebra. Integr. equ. oper. theory 62, 365–382 (2008). https://doi.org/10.1007/s00020-008-1629-y
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DOI: https://doi.org/10.1007/s00020-008-1629-y