## On Clifford Space and Higher Curvature Gravity

**Authors:** Carlos Castro

Clifford-space Gravity is revisited and new results are found. A derivation of the proper expressions for the connections (with $torsion$) in Clifford spaces ( $C$-spaces) is presented. The introduction of hyper-determinants of hyper-matrices are instrumental in the derivation of the $ C$-space generalized gravitational field equations from a variational principle and based on the extension of the Einstein-Hilbert-Cartan action. We conclude by pointing out the relations of Clifford space gravity to Lanczos-Lovelock-Cartan higher curvature gravity with torsion and extended gravitational theories based on $ f ( R ), f ( R_{\mu \nu} ), ... $ actions, for polynomial-valued functions. Introducing nonmetricity furnishes higher curvature extensions of metric affine theories of gravity.

**Comments:** 16 Pages. submitted to Foundations of Physics

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### Submission history

[v1] 2012-06-28 01:24:05

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