It claims that thermodynamic systems can be represented by Riemannian geometry, and that statistical properties can be derived from the model.
42.
It was not until much later that holonomy groups would be used to study Riemannian geometry in a more general setting.
43.
For instance, in relativity or Riemannian geometry, orthonormal frames are used to obtain a description of the Levi-Civita connection as a Cartan connection.
44.
His many other mathematical contributions include important theorems in Riemannian geometry and work on physics-related topics such as gauge theory and mirror symmetry.
45.
In Riemannian geometry geodesics are not the same as " shortest curves " between two points, though the two concepts are closely related.
46.
For example, the Hamilton Jacobi equations can be used to determine the geodesics on a Riemannian manifold, an important variational problem in Riemannian geometry.
47.
In order to include electromagnetism into the geometry of general relativity, Hermann Weyl worked to generalize the Riemannian geometry upon which general relativity is based.
48.
The transportation problem as it is stated in modern or more technical literature looks somewhat different because of the development of Riemannian geometry and measure theory.
49.
The length of the minor arc of a great circle is taken as the distance between two points on a surface of a sphere in Riemannian geometry.
50.
The notion of a directional derivative of a function from multivariable calculus is extended in Riemannian geometry to the notion of a covariant derivative of a tensor.
