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Möbius Group

The equation


represents an $n$-D Hypersphere $\Bbb{S}^n$ as a quadratic hypersurface in an $(n+1)$-D real projective space $\Bbb{P}^{n+1}$, where $x_a$ are homogeneous coordinates in $\Bbb{P}^{n+1}$. Then the Group $M(n)$ of projective transformations which leave $\Bbb{S}^n$ invariant is called the Möbius group.


Iyanaga, S. and Kawada, Y. (Eds.). ``Möbius Geometry.'' §78A in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 265-266, 1980.

© 1996-9 Eric W. Weisstein