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Projectively flat Finsler manifolds with infinite dimensional holonomy
-
Zoltán Muzsnay
and
Péter T. Nagy
Published/Copyright:
December 21, 2012
Abstract
Recently, we developed a method for the study of holonomy properties of non-Riemannian Finsler manifolds and obtained that the holonomy group cannot be a compact Lie group if the Finsler manifold of dimension >2 has non-zero constant flag curvature. The purpose of this paper is to move further, exploring the holonomy properties of projectively flat Finsler manifolds of non-zero constant flag curvature. We prove in particular that projectively flat Randers and Bryant–Shen manifolds of non-zero constant flag curvature have infinite dimensional holonomy group.
Funding source: Hungarian Scientific Research Fund (OTKA)
Award Identifier / Grant number: K 67617
Received: 2012-2-4
Revised: 2012-9-20
Published Online: 2012-12-21
Published in Print: 2015-3-1
© 2015 by De Gruyter
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- Frontmatter
- Near abelian profinite groups
- On Calabi–Yau threefolds associated to a web of quadrics
- On the partial fraction decomposition of the restricted partition generating function
- Projectively flat Finsler manifolds with infinite dimensional holonomy
- Weighted version of Carleson measure and multilinear Fourier multiplier
- Injective objects and retracts of Fraïssé limits
- On hypersurfaces containing projective varieties
- Additive reducts of algebraically closed valued fields
- On the subconvexity problem for GL(3) × GL(2) L-functions
- An algebraic property of Hecke operators and two indefinite theta series
- Sum formula of multiple Hurwitz-zeta values
- Classification of homogeneous holomorphic hermitian principal bundles over G/K
- Integrality properties of the CM-values of certain weak Maass forms
- Heat kernel for fractional diffusion operators with perturbations
- New class of multiple weights and new weighted inequalities for multilinear operators
- Balanced Hermitian geometry on 6-dimensional nilmanifolds
- Extensions of tame algebras and finite group schemes of domestic representation type
- Weighted estimates for multilinear Fourier multipliers
- Cluster tilting vs. weak cluster tilting in Dynkin type A infinity
- From ring epimorphisms to universal localisations
- Brauer algebras of type B
- Existence problems for the p-Laplacian
- Averaging operators over nondegenerate quadratic surfaces in finite fields
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Articles in the same Issue
- Frontmatter
- Near abelian profinite groups
- On Calabi–Yau threefolds associated to a web of quadrics
- On the partial fraction decomposition of the restricted partition generating function
- Projectively flat Finsler manifolds with infinite dimensional holonomy
- Weighted version of Carleson measure and multilinear Fourier multiplier
- Injective objects and retracts of Fraïssé limits
- On hypersurfaces containing projective varieties
- Additive reducts of algebraically closed valued fields
- On the subconvexity problem for GL(3) × GL(2) L-functions
- An algebraic property of Hecke operators and two indefinite theta series
- Sum formula of multiple Hurwitz-zeta values
- Classification of homogeneous holomorphic hermitian principal bundles over G/K
- Integrality properties of the CM-values of certain weak Maass forms
- Heat kernel for fractional diffusion operators with perturbations
- New class of multiple weights and new weighted inequalities for multilinear operators
- Balanced Hermitian geometry on 6-dimensional nilmanifolds
- Extensions of tame algebras and finite group schemes of domestic representation type
- Weighted estimates for multilinear Fourier multipliers
- Cluster tilting vs. weak cluster tilting in Dynkin type A infinity
- From ring epimorphisms to universal localisations
- Brauer algebras of type B
- Existence problems for the p-Laplacian
- Averaging operators over nondegenerate quadratic surfaces in finite fields
- Lawson homology for abelian varieties
