We describe extensions of several key concepts of differential geometry to manifolds with density, including curvature, the Gauss-Bonnet theorem and formula, geodesics, and constant curvature surfaces.
Professor Frank Morgan, Professor of Mathematics,Williams CollegeFrank.Morgan@williams.edu<
"Differential Geometry of Manifolds with Density,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 7
, Article 2.
Available at: https://scholar.rose-hulman.edu/rhumj/vol7/iss1/2