Abstract
We prove that the volume of PT 1, 0 z 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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Received: 11 March 2005
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Yan, R. On the volume of the projectivized tangent bundle in a complex Finsler manifold. Arch. Math. 86, 458–463 (2006). https://doi.org/10.1007/s00013-005-1498-4
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DOI: https://doi.org/10.1007/s00013-005-1498-4