例句與造句

1. In the theory of Lorentzian manifolds, Fermi Walker differentiation is a generalization of covariant differentiation.
2. Covariant differentiation of tensors was given a geometric interpretation by who introduced the notion of parallel transport on surfaces.
3. He was also influenced by the works of covariant differentiation that allowed Ricci-Curbastro to make the greatest progress.
4. Thus the theory of covariant differentiation forked off from the strictly Riemannian context to include a wider range of possible geometries.
5. Using ideas from Lie algebra cohomology, Koszul successfully converted many of the analytic features of covariant differentiation into algebraic ones.
6. It's difficult to find covariant differentiation in a sentence. 用covariant differentiation造句挺難的
7. To indicate covariant differentiation of any tensor field, a " semicolon " (; ) is placed before an added lower ( covariant ) index.
8. On the other hand, the notion of covariant differentiation was abstracted by Jean-Louis Koszul, who defined ( linear or Koszul ) connection on the tangent bundle.
9. Koszul's definition was subsequently adopted by most of the differential geometry community, since it effectively converted the " analytic " correspondence between covariant differentiation and parallel translation to an " algebraic " one.
10. In the 1940s, practitioners of differential geometry began introducing other notions of covariant differentiation in general vector bundles which were, in contrast to the classical bundles of interest to geometers, not part of the tensor analysis of the manifold.
11. In 1950, Jean-Louis Koszul unified these new ideas of covariant differentiation in a vector bundle by means of what is known today as a "'Koszul connection "'or a "'connection on a vector bundle " '.
12. where \ nabla _ \ mu denotes covariant differentiation with respect to the metric g _ { \ mu \ nu }, while V _ G, V _ \ mu, and V _ \ omega are the self-interaction potentials associated with the scalar fields.
13. In a famous 1869 paper on the equivalence problem for differential forms in " n " variables, published in Crelle's Journal, he introduced the fundamental technique later called covariant differentiation and used it to define the Riemann Christoffel tensor ( the most common method used to express the curvature of Riemannian manifolds ).