Biharmonic vector fields on pseudo-Riemannian manifolds
Biharmonic vector fields on pseudo-Riemannian manifolds
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DOI：
10.1016/j.geomphys.2018.04.003
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发表时间：
2018-08
影响因子：
1.5
通讯作者：
M. Markellos;H. Urakawa
中科院分区：
文献类型：
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作者：
M. Markellos;H. Urakawa
伪黎曼流形（M，g）上向量场的双能量定义为对应映射（M，g）<$（TM，gS）的双能量，其中切丛TM具有Sasaki度量gS.研究了约束变分问题，其中变分仅限于向量场，相应的临界点条件刻画了双调和向量场。我们提供的例子，双调和向量场的三维李群配备了左不变的洛伦兹度量和哥德尔宇宙。
The bienergy of a vector field on a pseudo-Riemannian manifold (M, g) is defined to be the bienergy of the corresponding map (M, g)↦(T M, g S), where the tangent bundle T M is equipped with the Sasaki metric g S. The constrained variational problem is studied, where variations are confined to vector fields, and the corresponding critical point condition characterizes biharmonic vector fields. We provide examples of biharmonic vector fields on three dimensional Lie groups equipped with a left-invariant Lorentzian metric and the Gödel universe.