Gauss's Lemma states that in a Riemannian manifold, the length of a geodesic depends only on the initial tangent vector and not on the particular parametrization of the geodesic. This principle highlights the relationship between geodesics and the curvature of the manifold, emphasizing how geodesics can be used to analyze the geometric properties of spaces. Additionally, it plays a key role in understanding geodesic deviation and the behavior of Jacobi fields, which describe how geodesics vary in proximity to one another.
congrats on reading the definition of Gauss's Lemma. now let's actually learn it.