On the volume of the projectivized tangent bundle in a complex Finsler manifold |
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Authors: | Rongmu Yan |
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Institution: | (1) School of Mathematical Sciences, Xiamen University, 361005, P. R. China |
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Abstract: | We prove that the volume of PT z 1, 0 M, calculated with respect to a Kähler metric induced by a complex Finsler structure, is a constant. This contrasts sharply with the situation in real Finsler geometry, where the volume of unit tangent sphere at each point x in a real Finsler manifold is in general a function of x. Furthermore, we point out that different metrics have different constants in general. |
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Keywords: | , |
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