Abstract:In this note we give a direct method to classify all stable forms on $\Bbb R^n$ as well as to determine their automorphism groups. We show that in dimensions 6, 7, 8 stable forms coincide with non-degenerate forms. We present necessary conditions and sufficient conditions for a manifold to admit a stable form. We also discuss rich properties of the geometry of such manifolds.
Keywords: stable forms, automorphism groups
AMS Subject Classification: 53C15