[Part of] The Geometry Lecturer's Song of Immodesty

 
I can specify isometries in non-Euclidean Geometries
And fiddle coefficients in the fundamental form.
While I winge and whine and waffle
I can calculate Christoffel
And deform my shapes continuously without them getting torn.
 
I can easily parametrise, tangentialise and normalise
Whatever nasty surfaces that you might care to name.
I can prove a brontosaurus homeomorphic to a torus
(Or a libra or aquarius, the principle's the same.)