2019/11/30 by Lei Zhang, Ming Xu, Zhang, Lei +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1912.00210
openalex publication_date 2019/11/30 · openalex created_date 2019/12/05 · openalex updated_date 2026/07/28
In this paper, we introduce the notion of standard homogeneous (α1,α2)-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 \mathfrakg, if there exists one generic standard g.o. (α1,α2)-metric, then all other standard homogeneous (α1,α2)-metrics are also g.o.. For standard homogeneous (α1,α2)-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. (α1,α2)-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. (α1,α2)-metrics on the three Wallach spaces, W6=SU(3)/T2, W12=Sp(3)/Sp(1)3 and W24=F4/Spin(8), must be the normal homogeneous Riemannian metrics.