11. The study of Riemannian manifolds constitutes the subject called Riemannian geometry . 12. Riemannian geometry studies Riemannian manifolds, smooth manifolds with a " Riemannian metric ".13. General Riemannian geometry falls outside the boundaries of the program. 14. It is unique by the fundamental theorem of Riemannian geometry . 15. Conformal geometry has a number of features which distinguish it from ( pseudo-) Riemannian geometry . 16. In particular, the fundamental theorem of Riemannian geometry is true of pseudo-Riemannian manifolds as well. 17. These are called ( geodesic ) normal coordinates, and are often used in Riemannian geometry . 18. Geodesics are commonly seen in the study of Riemannian geometry and more generally metric geometry. 19. This led him to study Riemannian geometry , and to formulate general relativity in this language. 20. The subject founded by this work is Riemannian geometry .
