对偶平坦(α,β)-度量的共形不变性

本文主要研究了两个(α,β)-度量之间的共形变换.证明了:若F是一个局部对偶平坦的正则(α,β)-度量且与度量■共形相关,即■,那么度量■也是一个局部对偶平坦的(α,β)-度量当且仅当共形变换是一个位似.进一步,在度量具有奇异性的情形,我们证明了两个局部对偶平坦广义Kropina度量之间的任一共形变换必然是一个位似.

The Conformal Invariances of the Dually Flat (α, β)-metrics

We study the conformal transformations between two (α, β)-metrics. We prove that, if F is a locally dually flat regular (α, β)-metric and is conformally related to F, that is, F=e^σ(x)F, then F is also a locally dually flat (α, β)-metric if and only if the conformal transformation is a homothety. Further, in the case with singularity, we prove that any conformal transformation between two locally dually flat general Kropina metrics must be a homothety.