Lanczos-Lovelock and f(R) Gravity from Clifford Space Geometry

A rigorous construction of Clifford-space Gravity is presented which is compatible with the Clifford algebraic structure and permits the derivation of the generalized connections in Clifford spaces (C-space) in terms of derivatives of the C-space metric. We continue by arguing how Lanczos-Lovelock higher curvature gravity can be embedded into gravity in Clifford spaces and suggest how this might also occur for extended gravitational theories based on f(R),f(R _μν ),… actions, for polynomial-valued functions. Black-strings and black-brane metric solutions in higher dimensions D>4 play an important role in finding specific examples.