发表机构
Department of Applied Mathematics, Graduate School of Science, Tokyo University of Science; Katsushika Division, Institute of Arts and Sciences, Tokyo University of Science（东京理科大学理工学研究科应用数学系; 东京理科大学理工学院葛饰校区）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明有限维实赋范空间中单位球面等距蕴含线性等距，通过Plücker收缩体和零拉格朗日恒等式回答Kadets-Martín问题。
AI 中文摘要
我们证明，具有等距单位球面的有限维实赋范空间是线性等距的，其中每个球面携带由环境范数诱导的距离。这回答了Kadets和Martín在有限维中的对象级问题，而不需要断言给定球面等距的线性延拓。我们为每个范数关联一族由有限维$\ell_\infty$空间中线性收缩的体积归一化极大子式生成的Plücker收缩体。零拉格朗日恒等式表明球面度量决定这些体。一个有限暴露面构造从凸化数据中恢复几乎赋范收缩，紧致性结合精确体积恒等式产生线性等距。
英文摘要
We prove that finite-dimensional real normed spaces with isometric unit spheres are linearly isometric, where each sphere carries the distance induced by the ambient norm. This answers the object-level question of Kadets and Martín in finite dimensions, without asserting linear extension of a prescribed sphere isometry. We associate with each norm a family of Plücker contraction bodies generated by volume-normalized maximal minors of linear contractions into finite-dimensional $\ell_\infty$ spaces. Null-Lagrangian identities show that the sphere metric determines these bodies. A finite exposed-face construction recovers almost-norming contractions from the convexified data, and compactness together with an exact volume identity yields a linear isometry.
Comments23 pages
