Vanishing Theorems for p-Harmonic Forms on Submanifolds in Spheres

Abstract

In this paper, we present some vanishing theorems for p-harmonic forms on -super stable complete submanifold M immersed in sphere Sn + m. When 2 ≤ 1 ≤ n-2, M has a flat normal bundle. Assuming that M is a minimal submanifold and δ > 1(n–1)p2 / 4n[p–1+(p–1)2kp], we prove a vanishing theorem for p-harmonic ℓ-forms.