&i&L&sup&p&/sup& p&/i&-Harmonic 1-Forms on &i&δ&/i&-Stable Hypersurface in Space Form with Nonnegative Bi-Ricci Curvature

摘要

In this paper, we investigate the space of L~(p) p -harmonic 1-forms on a complete noncompact orientable δ -stable hypersurface M~(m) that is immersed in space form with nonnegative BiRic curvature. We prove the nonexistence of L~(p) p -harmonic 1-forms on M~(m) . Moreover, we obtain some vanishing properties for this class of harmonic 1-forms.