In this note we present formulas that express the Euler characteristic of the set of real solutions of a system of quadric equations inequalities, and also some results that make it possible to use information about the solution sets of systems of quadric equations and inequalities to characterize the conditional extremum points of smooth functions.
Title: Computation of the Euler characteristic of intersections of real quadrics
Authors: A.A. Agrachev, R.V. Gamkrelidze
Journal title: Soviet Math. Dokl.
MathNet (ENG): http://mi.mathnet.ru/dan7735