CONSTRUCTION OF TRIHARMONIC MAPS

摘要

Theory of harmonic maps has been applied into various fields in differential geometry. By extending the notion of harmonic maps, J. Eel Is and L. Lemaire introduced polyharmonic maps of order k. In 1989, S. B. Wang showed the Euler Lagrange equation of polyharmonic maps of order 3 (triharmonic maps). In this paper, we study triharmonic immersion into a sphere. We show the necessary and sufficient condition of triharmonic isometric immersion such that Sigma(m)(s, t=1) del 1/UB(e(s), e(t)) = 0, for all vector field U, and give some non trivial examples. Moreover, we also construct non harmonic triharmonic maps.