Correction to “All regular Landsberg metrics are Berwald”
نویسندگان
چکیده
منابع مشابه
Some Remarks on Berwald Manifolds and Landsberg Manifolds
In the present paper, we shall prove new characterizations of Berwald spaces and Landsberg spaces. The main idea inthis research is the use of the so-called average Riemannian metric.
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Equality of hh -curvatures of the Berwald and Cartan connections leads to a new class of Finsler metrics, socalled BC-generalized Landsberg metrics. Here, we prove that every BC-generalized Landsberg metric of scalar flag curvature with dimension greater than two is of constant flag curvature.
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In Theorem 1, we generalize the results of Szabó [Sz1, Sz2] for Berwald metrics that are not necessary strictly convex: we show that for every Berwald metric F there always exists a Riemannian metric affine equivalent to F . Further, we investigate geodesic equivalence of Berwald metrics. Theorem 2 gives a system of PDE that has a (nontrivial) solution if and only if the given essentially Berwa...
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In Theorem 1, we generalize some results of Szabó [Sz1, Sz2] for Berwald metrics that are not necessarily strictly convex: we show that for every Berwald metric F there always exists a Riemannian metric affine equivalent to F . As an application we show (Corollary 3) that every Berwald projectively flat metric is a Minkowski metric; this statement is a “Berwald” version of Hilbert’s 4th problem...
متن کاملBerwald metrics constructed by Chevalley’s polynomials
Berwald metrics are particular Finsler metrics which still have linear Berwald connections. Their complete classification is established in an earlier work, [Sz1], of this author. The main tools in these classification are the Simons-Berger holonomy theorem and the Weyl-group theory. It turnes out that any Berwald metric is a perturbed-Cartesian product of Riemannian, Minkowski, and such non-Ri...
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ژورنال
عنوان ژورنال: Annals of Global Analysis and Geometry
سال: 2008
ISSN: 0232-704X,1572-9060
DOI: 10.1007/s10455-008-9131-y