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- Ioan BUCATARU, Zoltán MUZSNAY
- 2011

The projective metrizability problem can be formulated as follows: under what conditions the geodesics of a given spray coincide with the geodesics of some Finsler space, as oriented curves. In Theorem 3.8 we reformulate the projective metrizability problem for a spray in terms of a first-order partial differential operator P 1 and a set of algebraic… (More)

- ZOLTÁN MUZSNAY, Z. MUZSNAY
- 2008

In this paper we investigate the following question: under what conditions can a second-order homogeneous ordinary differential equation (spray) be the geodesic equation of a Finsler space. We show that the Euler-Lagrange partial differential system on the energy function can be reduced to a first order system on this same function. In this way we are able… (More)

The aim of this paper is to show that holonomy properties of Finsler manifolds can be very different from those of Riemannian manifolds. We prove that the holonomy group of a positive definite non-Riemannian Finsler manifold of non-zero constant curvature with dimension > 2 cannot be a compact Lie group. Hence this holonomy group does not occur as the… (More)

The aim of this paper is to show that the holonomy group of a non-Riemannian Finsler manifold of constant curvature with dimension n > 2 cannot be a compact Lie group and hence it cannot occur as the holonomy group of any Riemannian manifold. This result gives a positive answer to the following problem formulated by S. S. Chern and Z. Shen: Is there a… (More)

- Zoltán Muzsnay
- 2006

In this paper we study the linearizability problem for 3-webs on a 2-dimensional manifold. With an explicit computation based on the theory developed in [9], we examine a 3-web whose linearizability was claimed in [9]. We show that, contrary to the statement of [6] and [7], this particular web is linearizable. We compute explicitly the affine deformation… (More)

The geodesic graph of Riemannian spaces all geodesics of which are orbits of 1-parameter isometry groups is constructed by J. Szenthe in 1976 and it became a basic tool for studying such spaces, called g.o. spaces. This infinitesimal structure corresponds to the reductive complement m in the case of naturally reductive spaces. The systematic study of… (More)

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