ON THE PROBLEM OF NON-BERWALDIAN LANDSBERG SPACES
S. G. Elgendi
Abstract
We study the long-standing problem of the existence of non-Berwaldian Landsberg spaces from the perspective of conformal transformations. We calculate the Berwald and Landsberg tensors in terms of the T-tensor and show that there are Landsberg spaces with nonvanishing T-tensor. We give a necessary condition for a Landsberg space to be Berwaldian. We find conditions under which the Landsberg spaces cannot be Berwaldian and give examples of ( $y$ -local) non-Berwaldian Landsberg spaces.
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MathematicsPure mathematicsTensor (intrinsic definition)Conformal mapSpace (punctuation)Mathematical analysisLinguisticsPhilosophyAdvanced Differential Geometry ResearchOphthalmology and Eye Disorders