Metrizability of holonomy invariant projective deformation of sprays

In this paper, we consider projective deformation of the geodesic system of Finsler spaces by holonomy invariant functions: Starting by a Finsler spray $S$ and a holonomy invariant function $P$, we investigate the metrizability property of the projective deformation $\widetilde{S}=S-2\lambda P C$. We prove that for any holonomy invariant nontrivial function $P$ and for almost every value $\lambda\in R$, such deformation is not Finsler metrizable. We identify the cases where such deformation can lead to a metrizable spray: in these cases, the holonomy invariant function is necessarily one of the principal curvatures of the geodesic structure

Strict Forest Reserve Research in the Margin of the Carpathians, the Vár-hegy Case-Study

Sixteen forest reserves are situated in the northern part of Hungary which belongs to the Carpathian region according to EURAC delimitation (Ruffini et al. 2006). These Hungarian forest reserves expand the natural forest remnant/forest reserve net of the Carpathians towards the lower hilly region, representing the deciduous beech and oak forest belts near their lower (xeric) distribution limits. This paper outlines the Hungarian forest reserves belonging to the Carpathian region and the preliminary results of current projects in the Vár-hegy Forest Reserve (Bükk Mts., Hungary) as a case study. The alteration of tree species composition was investigated here based on the reconstruction of forest history in the previous 130 years (management period) and analyses of forest stand inventory. In another project CO2 sequestration changes of these forest stands were modeled since the clear-cutting in the 1880th and carbon stored in the forest ecosystem compartments was estimated. Our results show that the forest reserve stands are presently in a transition state from the managed forest towards a more natural mixed forest with several age-classes