Year: 2019
Type: preprint
Abstract: In this paper, we introduce the notion of standard homogeneous $(α_1,α_2)$-metrics, as a natural non-Riemannian deformation for the normal homogeneous Riemannian metrics. We prove that with respect to the given bi-invariant inner product and orthogonal decompositions for $\mathfrak{g}$, if there exists one generic standard g.o. $(α_1,α_2)$-metric, then all other standard homogeneous $(α_1,α_2)$-metrics are also g.o.. For standard homogeneous $(α_1,α_2)$-metrics associated with a triple of compact connected Lie groups, we can refine our theorem and get some simple algebraic equations as the criterion for the g.o. property. As the application of this criterion, we discuss standard g.o. $(α_1,α_2)$-metric from H. Tamaru's classication work, and find some new examples of non-Riemannian g.o. Finsler spaces which are not weakly symmetric. On the other hand, we also prove that all standard g.o. $(α_1,α_2)$-metrics on the three Wallach spaces, $W^6=SU(3)/T^2$, $W^{12}=Sp(3)/Sp(1)^3$ and $W^{24}=F_4/Spin(8)$, must be the normal homogeneous Riemannian metrics.
Source: arXiv (Cornell University)
Authors: Zhang, Lei, Xu, Ming
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: 李理论和组合方法在芬斯勒几何研究中的应用, G146394020
OpenAlex ID: W2991225804