【摘 要】
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An(α,β)-manifold(M,F)is a Finsler manifold with the Finsler metric F being defined by a Riemannian metric α and 1-form β on the manifold M.In this paper
【机 构】
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SichuanUniversity,P.R.China
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An(α,β)-manifold(M,F)is a Finsler manifold with the Finsler metric F being defined by a Riemannian metric α and 1-form β on the manifold M.In this paper,we classify n-dimensional(α,β)-manifolds(non-Randers type)which are positively complete and locally projectively flat.We show that the non-trivial class is that M is homeomorphic to the n-sphere Sn and(Sn,F)is projectively related to a standard spherical Riemannian manifold,and then we obtain some special geometric properties on the geodesics and scalar flag curvature of F on Sn,especially when F is a metric of general square type.
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