“…Briefly, we apply the pull-back formalism. Thus, for example, we re-prove our earlier result published in [8], where we used classical tensor calculus. The self-containedness of our exposition also means that we prove most of the classically well-known auxiliary results whose formulation and proof is not available (in our best knowledge) in our context.…”
Section: Landsberg Tensorsupporting
confidence: 71%
“…since P is homogeneous of degree 0. Now we verify by an index-free argument the following result of our above mentioned paper [8]: Proposition 7.7 If the stretch tensor of a Finsler manifold depends only on the position, then it vanishes identically, i.e., ∇ v Σ = 0 implies that Σ = 0.…”
“…Briefly, we apply the pull-back formalism. Thus, for example, we re-prove our earlier result published in [8], where we used classical tensor calculus. The self-containedness of our exposition also means that we prove most of the classically well-known auxiliary results whose formulation and proof is not available (in our best knowledge) in our context.…”
Section: Landsberg Tensorsupporting
confidence: 71%
“…since P is homogeneous of degree 0. Now we verify by an index-free argument the following result of our above mentioned paper [8]: Proposition 7.7 If the stretch tensor of a Finsler manifold depends only on the position, then it vanishes identically, i.e., ∇ v Σ = 0 implies that Σ = 0.…”
“…For the readers' convenience, we briefly summarize these basic technicalities in Section 2, and, partly, in Section 3. We follow the notation and conventions of reference [17] and, with some modifications, [5]. These papers also give some links to the classical approach.…”
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.
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