Finsler metrizability and Landsberg spaces in dimension two

• Autores: G. Thompson
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 76, Fasc. 3-4, 2010, págs. 411-424
• Idioma: inglés
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• Resumen

  • The problems of Finsler metrizability in dimension two is analyzed and solved completely. Thereafter the famous Landsberg problem concerning the existence of Landsberg spaces whose the sprays do not correspond to linear connection is consid- ered. It is argued in dimension two that the answer to this question is a±rmative and it is explained why it is di±cult to produce a concrete example. Some of the results are extended to arbitrary dimension and ¯nally a comparison is made with recent alternative investigations into the Landsberg problems.