Abstract
Just recently, incompleteness in the proof of the theorem appearing in the title [published in Szabó (Ann Glob Anal Geom, to appear, 2008)] has been discovered. Without this problematic part, the theorem is established only in the following restricted form: “A regular Finsler metric is Berwald if and only if it satisfies the dual Landsberg condition.” The incompleteness appears in proving that the original Landsberg condition implies the dual one.
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Szabó, Z.I.: All regular Landsberg metrics are Berwald. Ann. Glob. Anal. Geom. (2008) (to appear). http://dx.doi.org/10.1007/s10455-008-9115-y
Szabó Z.I.: Positive definite Berwald spaces (Structure theorems). Tensor N. S. 35, 25–39 (1981)
Szabó, Z.I.: Berwald metrics constructed by Chevalley’s polynomials. arXiv:math.DG/0601522 (2006)
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Szabó, Z.I. Correction to “All regular Landsberg metrics are Berwald”. Ann Glob Anal Geom 35, 227–230 (2009). https://doi.org/10.1007/s10455-008-9131-y
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DOI: https://doi.org/10.1007/s10455-008-9131-y