Triharmonic isometric immersions into a manifold of non-positively constant curvature
Triharmonic isometric immersions into a manifold of non-positively constant curvature
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DOI：
10.1007/s00605-014-0713-4
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发表时间：
2015-08-01
影响因子：
0.9
通讯作者：
Urakawa, Hajime
中科院分区：
文献类型：
--
作者：
Maeta, Shun;Nakauchi, Nobumitsu;Urakawa, Hajime
三调和映射是两个黎曼流形之间的光滑映射空间中3-能量的临界点。研究了三次调和等距浸入非正常曲率空间形式的广义Chen猜想。我们证明了，如果区域是完备的，并且张量场的4-能量和-范数都是有限的，那么这样的浸入是极小的。
A triharmonic map is a critical point of the 3-energy in the space of smooth maps between two Riemannian manifolds. We study the generalized Chen's conjecture for a triharmonic isometric immersion into a space form of non-positive constant curvature. We show that if the domain is complete and both the 4-energy of , and the -norm of the tension field , are finite, then such an immersion is minimal.