The Weyl geometric curvature tensor structure
|School||Capital Normal University|
|Keywords||Riemannian geometry Weyl geometry the curvature tensor|
The gravitational field is very well explained by Einstein’s theory, which accounts for it in terms of the curvature of space, the curvature of space required by Einstein’s theory can be discussed in terms of the notion of the parallel displacement of a vector, the transport of a vector around a closed loop by parallel displacement resulting in the final direction of the vector differing form its initial direction. Weyl’s generalization was to suppose that the final vector has a different length as well as a different direction which is a very well generalization of Riemannian space.In §1, first let’s review some main conclusions of curvature tensor in Riemannian geometry.In §2, mainly talk about the constructing of the curvature tensorIn §3, show the proving process of the proposition.In §4 , show the constructing process of the curvature tensor in Weyl-Hermitian geometry, which can be seen as the extension to the complex space.