Geodesic orbit Finsler spaces with K ≥ 0 and the (FP) condition
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Ming Xu
Abstract
We study the interaction between the g.o. property and certain flag curvature conditions. A Finsler manifold is called g.o. if each constant speed geodesic is the orbit of a one-parameter subgroup. Besides the non-negatively curved condition, we also consider the condition (FP) for the flag curvature, i.e. in any flag we find a flag pole such that the flag curvature is positive. By our main theorem, if a g.o. Finsler space (M, F) has non-negative flag curvature and satisfies (FP), then M is compact. If M = G/H where G has a compact Lie algebra, then the rank inequality rk 𝔤 ≤ rk 𝔥+1 holds. As an application,we prove that any even-dimensional g.o. Finsler space which has non-negative flag curvature and satisfies (FP) is a smooth coset space admitting a positively curved homogeneous Riemannian or Finsler metric.
Funding statement: This paper is supported by Beijing Natural Science Foundation (No. Z180004), NSFC (No. 11771331, No. 11821101), Capacity Building for Sci-Tech Innovation —+Fundamental Scientific Research Funds (No. KM201910028021).
Acknowledgements
The author sincerely thanks Fernando Galaz-Garcia, Yuri G. Nikonorov and Wolfgang Ziller for helpful discussions.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- An 𝔽p2-maximal Wiman sextic and its automorphisms
- Pseudo-algebraic Ricci solitons on Einstein nilradicals
- The wobbly divisors of the moduli space of rank-2 vector bundles
- Symmetries of complex analytic vector fields with an essential singularity on the Riemann sphere
- Betti numbers and pseudoeffective cones in 2-Fano varieties
- The generating rank of a polar Grassmannian
- The Beckman–Quarles theorem via the triangle inequality
- On Huisman’s conjectures about unramified real curves
- Geodesic orbit Finsler spaces with K ≥ 0 and the (FP) condition
- On the Segre invariant for rank two vector bundles on ℙ2
- Lifting coarse homotopies
- How to construct all metric f-K-contact manifolds
- An extremum problem for the power moment of a convex polygon contained in a disc
- Sharply transitive sets in PGL2(K)
Artikel in diesem Heft
- Frontmatter
- An 𝔽p2-maximal Wiman sextic and its automorphisms
- Pseudo-algebraic Ricci solitons on Einstein nilradicals
- The wobbly divisors of the moduli space of rank-2 vector bundles
- Symmetries of complex analytic vector fields with an essential singularity on the Riemann sphere
- Betti numbers and pseudoeffective cones in 2-Fano varieties
- The generating rank of a polar Grassmannian
- The Beckman–Quarles theorem via the triangle inequality
- On Huisman’s conjectures about unramified real curves
- Geodesic orbit Finsler spaces with K ≥ 0 and the (FP) condition
- On the Segre invariant for rank two vector bundles on ℙ2
- Lifting coarse homotopies
- How to construct all metric f-K-contact manifolds
- An extremum problem for the power moment of a convex polygon contained in a disc
- Sharply transitive sets in PGL2(K)
