Rotationally symmetric symmphonic maps
Rotationally symmetric symmphonic maps
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旋转对称交响乐图
DOI：
10.1007/s10455-022-09840-6
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发表时间：
2022
影响因子：
0.7
通讯作者：
Nobumitsu Nakauchi
中科院分区：
文献类型：
--
作者：
佐藤進;佐藤進;Nobumitsu Nakauchi;Nobumitsu Nakauchi
我们考虑黎曼流形之间的映射空间上的度量回调函数。调和图是能量泛函 E(f) 的驻点，它是目标流形度量的回拉轨迹的积分。我们的泛函是回调范数的一个积分。静止地图称为非交响地图（Kawai in Nonlinear Anal. 74: 2284-2295, 2011）、（Kawai in Differ. Geom. Appl. 44: 161-177, 2016）、（Misawa in Nonlinear Anal. 75: 5971-5974, 2012）、（Misawa in Calc. Var. 75: 5971-5974, 2012）。 (Misawa in Adv. Differ. Equ. 23: 693-724, 2018)、(Misawa in Equ. Appl. 2: 1-20, 2021)、(Misawa in Adv. Geom. 22: 23-31, 2022) （Nakauchi in Nonlinear Anal. 108: 87-98, 2014）和（Nakauchi in Ricerche di Matematica 60: 219-235, 2011）。在本文中，我们关注旋转对称地图。我们证明 4 维模型空间之间的任何旋转对称映射当且仅当它是共形映射时才是交响映射。
We consider a functional of pullbacks of metrics on the space of mapsfbetween Riemannian manifolds. Harmonic maps are stationary points of the energy functionalE(f) which is an integral of thetraceof the pullback of the metric of the target manifold byf. Our functionalis an integral of thenormof the pullback. Stationary maps forare called assymphonic maps(Kawai in Nonlinear Anal. 74: 2284-2295, 2011), (Kawai in Differ. Geom. Appl. 44: 161-177, 2016), (Misawa in Nonlinear Anal. 75: 5971-5974, 2012), (Misawa in Calc. Var. Part. Differ. Equ. 55: 1-20, 2016), (Misawa in Adv. Differ. Equ. 23: 693-724, 2018), (Misawa in Equ. Appl. 2: 1-20, 2021), (Misawa in Adv. Geom. 22: 23-31, 2022), (Nakauchi in Nonlinear Anal. 108: 87-98, 2014) and (Nakauchi in Ricerche di Matematica 60: 219-235, 2011). In this paper, we are concerned with rotationally symmetric maps. We prove that any rotationally symmetric map between 4-dimensional model spaces is a symphonic map if and only if it is a conformal map.