Classical Theorems in Riemannian Geometry
What follows is an incomplete list of the most classical theorems in Riemannian geometry. The choice is made depending on its importance, beauty, and simplicity of formulation. Most of the results can be found in the classic monograph by Jeff Cheeger and D. Ebin (see below).
The formulations given are far from being very exact or the most general. This list is oriented to those who already know the basic definitions and want to know what these definitions are about.
Read more about this topic: Riemannian Geometry
Famous quotes containing the words classical and/or geometry:
“Et in Arcadia ego.
[I too am in Arcadia.]”
—Anonymous, Anonymous.
Tomb inscription, appearing in classical paintings by Guercino and Poussin, among others. The words probably mean that even the most ideal earthly lives are mortal. Arcadia, a mountainous region in the central Peloponnese, Greece, was the rustic abode of Pan, depicted in literature and art as a land of innocence and ease, and was the title of Sir Philip Sidney’s pastoral romance (1590)
“I am present at the sowing of the seed of the world. With a geometry of sunbeams, the soul lays the foundations of nature.”
—Ralph Waldo Emerson (1803–1882)