Arithmetic Levi–Cività connection

Alexandru Buium ^[1]
1. [1] University of New Mexico
  
  University of New Mexico
  
  Estados Unidos
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 1, 2019
Idioma: inglés
DOI: 10.1007/s00029-019-0464-0
Enlaces
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Resumen
- This paper is part of a series of papers where an arithmetic analogue of classical differential geometry is being developed. In this arithmetic differential geometry functions are replaced by integer numbers, derivations are replaced by Fermat quotient operators, and connections (respectively curvature) are replaced by certain adelic (respectively global) objects attached to symmetric matrices with integral coefficients. Previous papers were devoted to an arithmetic analogue of the Chern connection. The present paper is devoted to an arithmetic analogue of the Levi–Civita connection.