Klein Surface


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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Klein Surface

 

Klein bottle, a closed one-sided surface, the concept for which was introduced by F. Klein in 1874.

A Klein surface can be made from a tube that is open at both ends by bending the tube, passing its narrower end through the

Figure 1. Klein surface

wall, and “identifying” the two end circles (see Figure 1,a). A surface is obtained that has a self-intersecting line (see Figure l,b). A Klein surface without self-intersection can only be realized in four-dimensional space.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
The maximum order of an automorphism of a Riemann surface of genus [greater than or equal to] 2 is 2g(M) + 1, and the maximum order of an automorphism of a non-orientable Klein surface of genus [greater than or equal to] 3 without boundary is g(M) + 1.