We introduce and study certain deformation of Minkowski norms in [Formula: see text] determined by a set linearly independent 1-forms smooth positive function variables. In particular, the Euclidean norm produces defined our recent work; its indicatrix is rotation hypersurface with text]-dimensional axis passing through origin. For text], generalizes construction text]-norms which form rich cla...

We study the structure of set algebraic curvature operators satisfying a sectional bound under light emerging field Convex Algebraic Geometry. More precisely, we determine in which dimensions $n$ this convex semialgebraic is spectrahedron or spectrahedral shadow; particular, for $n\geq5$, these give new counter-examples to Helton--Nie Conjecture. Moreover, efficient algorithms are provided if $...