Affine connections, midpoint formation, and point reflection

Anders Kock

doi:10.1016/j.tcs.2010.12.037

Affine connections, midpoint formation, and point reflection

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Abstract

We describe some differential-geometric structures in combinatorial terms: namely affine connections and their torsion and curvature, and we show that torsion free affine connections may equivalently be presented in terms of some simpler combinatorial structure: midpoint formation, and point reflection (geodesic symmetry). The method employed is that of synthetic differential geometry, which is briefly explained.

Original language	English
Journal	Theoretical Computer Science
Volume	412
Issue	36
Pages (from-to)	4770-4777
Number of pages	8
ISSN	0304-3975
DOIs	https://doi.org/10.1016/j.tcs.2010.12.037
Publication status	Published - 2011

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title = "Affine connections, midpoint formation, and point reflection",

abstract = "We describe some differential-geometric structures in combinatorial terms: namely affine connections and their torsion and curvature, and we show that torsion free affine connections may equivalently be presented in terms of some simpler combinatorial structure: midpoint formation, and point reflection (geodesic symmetry). The method employed is that of synthetic differential geometry, which is briefly explained.",

author = "Anders Kock",

year = "2011",

doi = "10.1016/j.tcs.2010.12.037",

language = "English",

volume = "412",

pages = "4770--4777",

journal = "Theoretical Computer Science",

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AU - Kock, Anders

PY - 2011

Y1 - 2011

N2 - We describe some differential-geometric structures in combinatorial terms: namely affine connections and their torsion and curvature, and we show that torsion free affine connections may equivalently be presented in terms of some simpler combinatorial structure: midpoint formation, and point reflection (geodesic symmetry). The method employed is that of synthetic differential geometry, which is briefly explained.

AB - We describe some differential-geometric structures in combinatorial terms: namely affine connections and their torsion and curvature, and we show that torsion free affine connections may equivalently be presented in terms of some simpler combinatorial structure: midpoint formation, and point reflection (geodesic symmetry). The method employed is that of synthetic differential geometry, which is briefly explained.

U2 - 10.1016/j.tcs.2010.12.037

DO - 10.1016/j.tcs.2010.12.037

M3 - Journal article

SN - 0304-3975

VL - 412

SP - 4770

EP - 4777

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 36

ER -

Affine connections, midpoint formation, and point reflection

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