Geometric Construction of the Levi-Civita Parallelism

Anders Kock

Dedicated to Bill Lawvere on the occasion of his 60th birthday

In terms of synthetic differential geometry, we give a variational characterization of the connection (parallelism) associated to a pseudo-Riemannian metric on a manifold.

Keywords: quadratic differential form, affine connection, synthetic differential geometry.

1991 MSC: 18F99, 53B20, 58A03.

Theory and Applications of Categories, Vol. 4, 1998, No. 9, pp 195-207.

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