The December 2020 Issue of the
American Mathematical Monthly (published by the Mathematical Association of America, and now available online at maa.org) features an article by Tevian Dray:
"Using Embedding Diagrams to Visualize Curvature".
Abstract: We give an elementary treatment of the curvature of surfaces of revolution in the language of vector calculus, using differentials rather than an explicit parameterization. We illustrate some basic features of curvature using embedding diagrams, and then use such a diagram to analyze the geometry of the Schwarzschild black hole.