Albedo formula_5 (also called blue-sky albedo) can then be given as: Directional-hemispherical reflectance is sometimes referred to as black-sky albedo and bi-hemispherical reflectance as white-sky albedo. These terms are important because they allow the albedo to be calculated for any given illumination conditions from a knowledge of the intrinsic properties of the surface. The albedos of planets, satellites and minor planets such as asteroids can be used to infer much about their properties. The study of albedos, their dependence on wavelength, lighting angle ("phase angle"), and variation in time comprises a major part of the astronomical field of photometry. For small
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