Intrinsic Differential Geometry with Geometric Calculus

摘要

Setting up a symbolic algebraic system is the first step in mathematics mechanization of any branch of mathematics. In this paper, we establish a compact symbolic algebraic framework for local geometric computing in intrinsic differential geometry, by choosing only the Lie derivative and the covariant derivative as basic local differential operators. In this framework, not only geometric entities such as the curvature and torsion of an affine connection have elegant representations, but their involved local geometric computing can be simplified.