On Rund's connection
We show that the holomorphic curvature (associated with a complex Finsler metric F)in the sense of M. Suzuki,  ,and B. Wong,, is (in the smooth case) precisely the holomorphic curvature of a connection essentially due to H. Rund,  (and reproposed in the bundle-theoretic setting by S. Kobayashi, ). We prove a complex analogue of Deike's theorem in real Finsler geometry. The indicatrix in each fibre of a convex complex Finsler bundle is shown to be an extrinsic sphere.
DOI Code: 10.1285/i15900932v15n1p85
Classification: 51H10; 51H20; 51A35
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