We introduce a new class of special Finsler manifolds, the class of p-Berwald manifolds. P-Berwald manifolds are defined as Finsler manifolds for which the projected Berwald curvature vanishes. We show that an at least 3-dimensional Finsler manifold is a p-Berwald manifold if and only if it is a weakly Berwald Douglas manifold. 2-dimensional p-Berwald manifolds are characterized by means of a differential equation concerning the main scalar. We prove that a p-Berwald manifold is R-quadratic if and only if its stretch tensor vanishes.
Currently he is a temporary lecturer at the University of Debrecen. His research interests are classical and modern projective geometry and related topics.
Using the Cayley-Klein model of hyperbolic geometry and the tools of projective geometry, we present elementary proofs for the hyperbolic versions of some classical theorems on triangles. We show, in particular, that hyperbolic triangles have no Euler line.
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