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Additional info for Current Developments in Differential Geometry and its Related Fields: Proceedings of the 4th International Colloquium on Differential Geometry and its Related Fields

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Vm(p+q) ) with positive integer m, we say it is a (p, q)-bicolored path if its subpaths γi = (v(i−1)(p+q) , . . , vi(p+q) ), i = 1, . . , m, are (p, q)-primitive bicolored paths. We consider (p, q)-bicolored paths are motions of charged particles under a magnetic field of strength q/p. Under the influence of a magnetic field of strength q/p, a p-step path on the principal graph is bended and its terminus reaches to the terminus of a (p, q)-primitive bicolored path whose first p-step coincides with the given path.

Liang, Non-naturally reductive Einstein metrics on the compact simple Lie group F4 , Ann. Glob. Anal. Geom. 46, 103– 115 (2014). 7. J. E. D’Atri and W. S. 19 (215) (1979). 8. K. Mori, Left Invariant Einstein Metrics on SU (N ) that are not Naturally Reductive, Master Thesis (in Japanese) Osaka University 1994, English Translation: Osaka University RPM 96010 (preprint series) 1996. 9. Yu. G. Nikonorov, E. D. Rodionov and V. V. Slavskii, Geometry of Homogeneous Riemannian Manifolds, J. Math. Sci.

Yu. G. Nikonorov, E. D. Rodionov and V. V. Slavskii, Geometry of Homogeneous Riemannian Manifolds, J. Math. Sci. ) 146(6), 6313– 6390 (2007). 10. J-S. Park and Y. Sakane, Invariant Einstein metrics on certain homogeneous spaces, Tokyo J. Math. 20(1), 51–61 (1997). 11. M. Wang, Einstein metrics from symmetry and bundle constructions, in Surveys in Differential Geometry: Essays on Einstein Manifolds, Surv. Diff. Geom. VI, Int. Press, Boston, MA 1999. 12. M. -S. Chern, Advanced Lectures in Mathematics, vol.

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