发表机构
Isfahan University of Technology; Institute for Research in Fundamental Sciences（伊斯法罕理工大学; 基础科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对切丛上慢衰减渐近平坦度量，证明了其正质量定理与刚性定理，确定了广义渐近质量由底流形几何数据决定。
AI 中文摘要
设$(M,g)$为一渐近平坦流形，其切丛$TM$微分同胚于渐近平坦欧氏空间。我们针对$TM$上一类自然的、具有慢渐近衰减的渐近平坦度量$\tilde{g}$，证明了正质量定理与正质量刚性定理。这类度量通过沿$TM$的水平分布，在无穷远处将欧氏度量与基度量$g$插值构造而成。主要难点在于，$TM$上的诱导度量在$2n$维下衰减至ADM质量的标准阈值以下；但我们证明其渐近质量在广义意义上是良定义的，且由底流形$M$上的几何数据决定。
英文摘要
Let $(M,g)$ be an asymptotically flat manifold such that its tangent bundle $TM$ is diffeomorphically asymptotically Euclidean. We prove a positive mass theorem and a positive mass rigidity theorem for a natural class of asymptotically flat metrics $\widetilde g$ on $TM$ exhibiting slow asymptotic decay. These metrics are constructed by interpolating, along the horizontal distribution of $TM$, between the Euclidean metric and the base metric $g$ near infinity. The main difficulty is that the induced metrics on $TM$ decay below the standard threshold for the ADM mass in dimension $2n$; nevertheless, we show that their asymptotic mass is well-defined in a generalized sense and is determined by geometric data on the underlying manifold $M$.
Comments18 pages, no figures
