Martian surface Martian surface The study of surface characteristics (or surface properties and processes) is a broad category of Mars science that examines the nature of the materials making up the Martian surface. The study evolved from telescopic and remote-sensing techniques developed by astronomers to study planetary surfaces. However, it has increasingly become a subdiscipline of geology as automated spacecraft bring ever-improving resolution and instrument capabilities. By using characteristics such as color, albedo, and thermal inertia and analytical tools such as reflectance spectroscopy and radar, scientists are able to study the chemistry and physical makeup (e.g., grain sizes, surface roughness, and rock
Riemannian connection on a surface Riemannian connection on a surface embedded in Euclidean space "E" is just the pullback under the Gauss map of the Riemannian connection on "S". Using the identification of "S" with the homogeneous space SO(3)/SO(2), the connection 1-form is just a component of the Maurer–Cartan 1-form on SO(3). In other words, everything reduces to understanding the 2-sphere properly. For a surface "M" embedded in E (or more generally a higher-dimensional Euclidean space), there are several equivalent definitions of a vector field "X" on "M": The last condition means that the assignment "f" "Xf" on "C"("M") satisfies the Leibniz rule The space