  For a hypersurface V of a conformal space, we introduce a conformal
differential invariant I = h^2/g, where g and h are the first and the second
fundamental forms of V connected by the apolarity condition. This invariant is
called the conformal quadratic element of V. The solution of the problem of
conformal rigidity is presented in the framework of conformal differential
geometry and connected with the conformal quadratic element of V. The main
theorem states:
  Let n \geq 4 and V and V' be two nonisotropic hypersurfaces without umbilical
points in a conformal space C^n or a pseudoconformal space C^n_q of signature
(p, q), p = n - q. Suppose that there is a one-to-one correspondence f: V --->
V' between points of these hypersurfaces, and in the corresponding points of V
and V' the following condition holds: I' = f_* I, where f_*: T (V) ---> T (V)
is a mapping induced by the correspondence f. Then the hypersurfaces V and V'
are conformally equivalent.
