On a class of locally dually flat Finsler metrics of isotropic flag curvature

• Autores: Qiaoling Xia
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 78, Fasc. 1, 2011, pág. 12
• Idioma: inglés
• DOI: 10.5486/pmd.2011.4724
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• Resumen

  • In this paper, we characterize a class of locally dually at (á, â) metrics F = á + .â + k 2 de ned by a Riemannian metric á and a non-zero 1-form â, where .

    and k are non-zero constants. As an application, we prove that there is no locally dually at metric in the form F = á + .â + k 2 (. .= 0, k .= 0, â .= 0) with isotropic S-curvature unless it is Minkowskian. Moreover, we prove that if F = á + .â + k 2 (. .= 0, k .= 0, â .= 0) is locally dually at, then it is locally projectively at if and only if it is of constant ag curvature, and there is no locally dually at metrics in the form F = á +.â + k 2 (. .= 0, k .= 0, â .= 0) of isotropic ag curvature unless it is Minkowskian.