Characterization and structure of Finsler spaces with constant flag curvature |
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Authors: | Xiaohuan Mo |
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Institution: | (1) School of Mathematical Sciences, Peking University, 100871 Beijing, China |
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Abstract: | The geometric characterization and structure of Finsler manifolds with constant flag curvature (CFC) are studied. It is proved
that a Finsler space has constant flag curvature 1 (resp. 0) if and only if the Ricci curvature along the Hilbert form on
the projective sphere bundle attains identically its maximum (resp. Ricci scalar). The horizontal distributionH of this bundle is integrable if and only ifM has zero flag curvature. When a Finsler space has CFC, Hilbert form’s orthogonal complement in the horizontal distribution
is also integrable. Moreover, the minimality of its foliations is equivalent to given Finsler space being Riemannian, and
its first normal space is vertical
Project supported by Wang KC Fundation of Hong Kong and the National Natural Science Foundation of China (Grant No. 19571005). |
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Keywords: | Finsler space flag curvature projective sphere bundle |
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