History of Manifold

	Revision 26 . . (edit) November 4, 2001 4:02 pm by The Cunctator
	Revision 25 . . October 1, 2001 4:54 am by AxelBoldt [remove repetition]
	Revision 24 . . September 30, 2001 9:20 pm by (logged).29.241.xxx [it's not a lie group if the operations are not differentiable]

---

Difference (from prior major revision) (minor diff, author diff)

Changed: 2c2

manifolds serve as the phase space in classical mechanics; four dimensional pseudo-Riemannian manifolds are used to model spacetime in general relativity. What follows is a clean mathematical treatment of manifolds.

manifolds serve as the phase space in classical mechanics; four dimensional pseudo-Riemannian manifolds are used to model spacetime in general relativity. What follows is a clean mathematical treatment of manifolds.

Changed: 19,21c19

Manifolds are important because they provide the proper generalization of surfaces. In classical mechanics, the state space of systems with constraints are often modelled as manifolds. The theory of general relativity postulates that all of spacetime is a 4-manifold; in fact it is a [pseudo-Riemannian manifold]? which allows one to define angles, lengths and curvature. If a manifold also carries an infinitely differentiable group structure, it is called a Lie group. These are the proper objects for describing symmetries of analytical structures.

If a C∞ manifold also carries an infinitely often differentiable group structure, it is called a Lie group. These are the proper objects for describing symmetries of analytical structures.

Changed: 24c22

/Talk?

/Talk?