Riemannian geometry, a concept first generalized in the 19th century by Bernhard Riemann, deals with a broad range of geometries with various point to point metric properties.
Riemannian geometry was first put forward in generality by Bernhard Riemann in the 19th century. It deals with a broad range of geometries whose metric properties vary from point to point, including the standard types of non-Euclidean geometry. 
