Communications in Analysis and Geometry

Volume 28 (2020)

Number 8

The Second of Two Special Issues in Honor of Karen Uhlenbeck’s 75th Birthday

Special-Issue Editors: Georgios Daskalopoulos (Brown University), Kefeng Liu, Chuu-Lian Terng (U. of Cal. Irvine), and Shing-Tung Yau

Geodesic orbit spaces in real flag manifolds

Pages: 1933 – 2003

DOI: https://dx.doi.org/10.4310/CAG.2020.v28.n8.a7

Authors

Brian Grajales (Departamento de Matemática, IMECC-Unicamp, Cidade Universitária Zeferino Vaz., Campinas, SP, Brazil)

Lino Grama (Departamento de Matemática, IMECC-Unicamp, Cidade Universitária Zeferino Vaz., Campinas, SP, Brazil)

Caio J. C. Negreiros (Departamento de Matemática, IMECC-Unicamp, Cidade Universitária Zeferino Vaz., Campinas, SP, Brazil)

Abstract

We describe the invariant metrics on real flag manifolds and classify those with the following property: every geodesic is the orbit of a one-parameter subgroup. Such a metric is called g.o. (geodesic orbit). In contrast to the complex case, on real flag manifolds the isotropy representation can have equivalent submodules, which makes invariant metrics depend on more parameters and allows us to find more cases in which non-trivial g.o. metrics exist.

Full Text (PDF format)

Received 30 November 2018

Accepted 9 October 2020

Published 8 January 2021