Abstract: We obtained one sufficient condition under which a 2-harmonic submanifold with nonnegative sectioncurvature turns into a maximal submanifold by promoting known theorem. And We also studied the 2-harmonic hypersurfaces by weakening the conditions when the Ricci curvature of the ambient manifold had upper and lower restrict, thus improving the known results.

Key words: pseudoRiemann manifold, 2-harmonic map, mean curvature vector, spacelike submanifold, hypersurface