»ã±¨±êÌâ (Title)£º A new quantity in Finsler geometry

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»ã±¨ÈË (Speaker)£ºÄªÓ×»¶£¨±±¾©´óѧ£©

»ã±¨¹¦·ò (Time)£º2024Äê1ÔÂ17ÈÕ(ÖÜÈý) 16:00-17:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿GJ303

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»ã±¨ÌáÒª£ºIn this lecture, we discuss a new Finslerian quantity defined by the -curvature and the angular metric tensor. We show that the -curvature not only gives a measure of the failure of a Finsler metric to be of scalar flag curvature and but also has vanishing trace. We find that the -curvature is closed related the Riemann curvature, the Matsumoto torsion and the -curvature. We answer Z. Shen's an open problem in terms of the -curvature. Finally, we give a global rigidity result for Finsler metrics of negative Ricci curvature on a compact manifold via the -curvature, generalizing a theorem previously only known in the case of negatively curved Finsler metrics with scalar flag curvature.