For n=4, the real roots of the y-discriminant of det(R-xI-yK) locate the critical values of sectional curvature, exactly on the dense open set where the discriminant of that polynomial is nonzero.
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Algebraic conditions for the positivity of sectional curvature
For n=4, the real roots of the y-discriminant of det(R-xI-yK) locate the critical values of sectional curvature, exactly on the dense open set where the discriminant of that polynomial is nonzero.