On the existence of pseudoharmonic maps from pseudohermitian manifolds into riemannian manifolds with nonpositive sectional curvature

SHU-CHENG CHANGChang, T.-H.T.-H.Chang2018-09-102018-09-10201310936106http://www.scopus.com/inward/record.url?eid=2-s2.0-84884309451&partnerID=MN8TOARShttp://scholars.lib.ntu.edu.tw/handle/123456789/377627https://www.scopus.com/inward/record.uri?eid=2-s2.0-84884309451&doi=10.4310%2fAJM.2013.v17.n1.a1&partnerID=40&md5=55233ae24a337e17be60e1adef280fe5In this paper, we first derive a CR Bochner identity for the pseudoharmonic map heat flow on pseudohermitian manifolds. Secondly, we are able to prove existence of the global solution for the pseudoharmonic map heat flow from a closed pseudohermitian manifold into a Riemannian manifold with nonpositive sectional curvature. In particular, we prove the existence theorem of pseudoharmonic maps. This is served as the CR analogue of Eells-Sampson's Theorem for the harmonic map heat flow. © 2013 International Press.CR Bochner identity; Energy density; Folland-Stein space; Pseudoharmonic map; Pseudoharmonic map heat flow; Pseudohermitian manifold; Pseudohermitian Ricci tensors; Pseudohermitian torsion; Sub-LaplacianOn the existence of pseudoharmonic maps from pseudohermitian manifolds into riemannian manifolds with nonpositive sectional curvaturejournal article10.4310/AJM.2013.v17.n1.a12-s2.0-84884309451WOS:000317584400001