Arithmetic analogues of some basic concepts from Riemannian geometry

Alexandru Buium

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arXiv · 1503.02489

Arithmetic analogues of some basic concepts from Riemannian geometry

Alexandru Buium

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Abstract

Following recent work of the author, partly in collaboration with T. Dupuy and M. Barrett, we describe arithmetic analogues of some key concepts from Riemannian geometry such as: metrics, Chern connections, curvature, etc. Theorems are stated to the effect that the spectrum of the integers has a non-vanishing curvature.

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Alexandru Buium. 2015-03-09. Arithmetic analogues of some basic concepts from Riemannian geometry. https://arxiv.org/abs/1503.02489

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