Much of his research concerns the Riemannian geometry of 4-manifolds, or related topics in complex and differential geometry.
32.
These would subsequently become major parts of the theories of Riemannian geometry, algebraic geometry, and complex manifold theory.
33.
Modern geometry has many ties to physics as is exemplified by the links between pseudo-Riemannian geometry and general relativity.
34.
However, ordinary Riemannian geometry is unable to describe the properties of the electromagnetic field as a purely geometric phenomenon.
35.
Barrett O'Neill's Semi-riemannian geometry ).
36.
In Riemannian geometry, the existence of a metric chooses a unique preferred torsion-free covariant derivative, known as the Levi-Civita connection.
37.
His mathematican contributions include comparison theorems of Laplacian eigenvalues on Riemannian manifolds and the maximal diameter theorem in Riemannian geometry.
38.
It's a nice springboard into Riemannian geometry, should you decide to take that at a later date, or general relativity.
39.
Using Riemannian geometry Holland formulated this method in very general terms that includes as special cases quantum many-particle systems and spin.
40.
Here is a short list of global results concerning manifolds with positive Ricci curvature; see also classical theorems of Riemannian geometry.
