Hairy ball theorem

The hairy ball theorem (also called the law of combed hedgehog known in English hairy ball theorem ) or problem of the global wind is a result from the mathematical branch of differential topology. This statement is also set of Poincaré - Brouwer called because Luitzen Egbertus January Brouwer has proved this in 1912 with the help of the theorem of Poincaré.

Hairy ball theorem

In particular, there is not such a vector field on the 2-sphere ( the surface of the three-dimensional sphere), from which the following mnemonic follows:

Such a bald spot is also referred to as a " bald spot ".

If one interprets the hairy ball theorem physically, so in principle can not fly anywhere on Earth at the same time wind for the same reason - it must be on the surface of a three-dimensional spherical planet always windless digits show ( hence the name: the problem of global wind ). A flat surface, however, can be easily combed steadily without bald patches; as a torus.

The hairy ball theorem is an illustration of the theorem of Poincaré - Hopf.

Swell

• R. Abraham, Jerrold E. Marsden, T. Ratiu: Manifolds, tensor analysis, and applications ( Applied mathematical sciences = 75). 2nd edition. Springer, New York, NY, among others, 1988, ISBN 0-387-96790-7.