Translator Disclaimer
October 2020 Equigeodesics on generalized flag manifolds with ${\rm G}_2$-type $\mathfrak{t}$-roots
Marina Statha
Osaka J. Math. 57(4): 871-888 (October 2020).

Abstract

We study homogeneous curves in generalized flag manifolds $G/K$ with ${\rm G}_2$-type $\mathfrak{t}$-roots, which are geodesics with respect to each $G$-invariant metric on $G/K$. These curves are calledequigeodesics. The tangent space of such flag manifolds splits into six isotropy summands, which are in one-to-one correspondence with $\mathfrak{t}$-roots. Also, these spaces are a generalization of the exceptional full flag manifold ${\rm G}_2/T$. We give a characterization for structural equigeodesics for flag manifolds with ${\rm G}_2$-type $\mathfrak{t}$-roots, and we give for each such flag manifold, a list of subspaces in which the vectors are structural equigeodesic vectors.

Citation

Download Citation

Marina Statha. "Equigeodesics on generalized flag manifolds with ${\rm G}_2$-type $\mathfrak{t}$-roots." Osaka J. Math. 57 (4) 871 - 888, October 2020.

Information

Published: October 2020
First available in Project Euclid: 9 October 2020

MathSciNet: MR4160339

Subjects:
Primary: 53C25
Secondary: 13P10, 53C30, 65H10, 68W30

Rights: Copyright © 2020 Osaka University and Osaka City University, Departments of Mathematics

JOURNAL ARTICLE
18 PAGES


SHARE
Vol.57 • No. 4 • October 2020
Back to Top