Rational approximation to real points on quadratic hypersurfaces.

Let Z be a quadratic hypersurface of Pn(R) defined over Q containing points whose coordinates are linearly independent over Q. We show that, among these points, the largest exponent of uniform rational approximation is the inverse 1/ρ of an explicit Pisot number ρ<2 depending only on n if the Witt index (over Q) of the quadratic form q defining Z is at most 1, and that it is equal to 1 otherwise. Furthermore, there are points of Z which realize this maximum. They constitute a countably infinite set in the first case, and an uncountable set in the second case. The proof for the upper bound 1/ρ uses a recent transference inequality of Marnat and Moshchevitin. In the case n=2, we recover results of the second author while for n>2, this completes recent work of Kleinbock and Moshchevitin. [ABSTRACT FROM AUTHOR]