Abstract
In this paper, we introduce the flag-wise positively curved condition for Finsler spaces (the (FP) condition), which means that in each tangent plane, there exists a flag pole in this plane such that the corresponding flag has positive flag curvature. Applying the Killing navigation technique, we find a list of compact coset
spaces admitting non-negatively curved homogeneous Finsler metrics
satisfying the (FP) condition. Using a crucial technique we developed previously, we prove that most of these coset spaces cannot be endowed with positively curved homogeneous Finsler metrics. We also prove that any
Lie group whose Lie algebra is a rank 2 non-Abelian compact Lie algebra
admits a left invariant Finsler metric satisfying the (FP) condition.
As by-products, we find
the first example of non-compact coset space
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11771331
Award Identifier / Grant number: 11671212
Award Identifier / Grant number: 51535008
Funding source: Natural Science Foundation of Beijing Municipality
Award Identifier / Grant number: 1182006
Funding statement: Supported by NSFC (no. 11771331, 11671212, 51535008), Beijing Natural Science Foundation (no. 1182006) and the Fundamental Research Funds for the Central Universities.
Acknowledgements
We would like to thank W. Ziller and L. Huang for helpful comments and discussions. This work is dedicated to the 80th birthday of our most respectable friend, teacher of mathematics and life, Professor Joseph A. Wolf.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- The Mackey problem for free locally convex spaces
- Restricted averaging operators to cones over finite fields
- Asymptotic expansion of holonomy
- Compactness criteria for real algebraic sets and Newton polyhedra
- Unit-graphs and special unit-digraphs on matrix rings
- ϕ-amenability and character amenability of Fréchet algebras
- Dirichlet series of two variables, real analytic Jacobi–Eisenstein series of matrix index, and Katok–Sarnak type result
- Idempotence of finitely generated commutative semifields
- N-Lusin property in metric measure spaces: A new sufficient condition
- Group schemes and local densities of ramified hermitian lattices in residue characteristic 2. Part II
- Homogeneous Finsler spaces and the flag-wise positively curved condition
- Index of Grassmann manifolds and orthogonal shadows
- Jantzen filtration and strong linkage principle for modular Lie superalgebras
- On the maximum conjecture
Artikel in diesem Heft
- Frontmatter
- The Mackey problem for free locally convex spaces
- Restricted averaging operators to cones over finite fields
- Asymptotic expansion of holonomy
- Compactness criteria for real algebraic sets and Newton polyhedra
- Unit-graphs and special unit-digraphs on matrix rings
- ϕ-amenability and character amenability of Fréchet algebras
- Dirichlet series of two variables, real analytic Jacobi–Eisenstein series of matrix index, and Katok–Sarnak type result
- Idempotence of finitely generated commutative semifields
- N-Lusin property in metric measure spaces: A new sufficient condition
- Group schemes and local densities of ramified hermitian lattices in residue characteristic 2. Part II
- Homogeneous Finsler spaces and the flag-wise positively curved condition
- Index of Grassmann manifolds and orthogonal shadows
- Jantzen filtration and strong linkage principle for modular Lie superalgebras
- On the maximum conjecture