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Equigeodesics on Generalized Flag Manifolds with Four Isotropy Summands

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Abstract

A curve of the form \(\gamma (t) = (exp tX)\cdot o\) is called equigeodesic on homogeneous space G/K if it is a geodesic with respect to each invariant metric on G/K. In this article, we study equigeodesics on generalized flag manifolds with four isotropy summands, and give examples of structural equigeodesics on generalized flag manifolds of the exceptional Lie groups \(F_4, E_6, E_7\) with four isotropy summands.

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Acknowledgements

This research was supported by Natural Science Foundation of Anhui province (No. 2008085QA03). The author expresses her sincere thanks to the referees for their comments which improved the paper.

Funding

Funding was provided by Natural Science Foundation of Anhui Province (Grant No. 2008085QA03).

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  1. School of Microelectronics and Data Science, Anhui University of Technology, Maanshan, 243032, People’s Republic of China

    Na Xu

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  1. Na Xu
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Correspondence to Na Xu.

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Xu, N. Equigeodesics on Generalized Flag Manifolds with Four Isotropy Summands. Results Math 78, 82 (2023). https://doi.org/10.1007/s00025-023-01861-2

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