Stability of stationary maps of a functional related to pullbacks of metrics
Stability of stationary maps of a functional related to pullbacks of metrics
复制标题
与指标回调相关的函数平稳图的稳定性
DOI：
10.1016/j.difgeo.2015.11.005
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发表时间：
2016
影响因子：
0.5
通讯作者：
Shigeo Kawai and Nobumitsu Nakauchi
中科院分区：
文献类型：
--
作者：
Kei Kondo;Minoru Tanaka;Shigeo Kawai and Nobumitsu Nakauchi
Abstract Let (M, g) and (N, h) be Riemannian manifolds without boundary. We consider the functional Φ (f)=∫ M‖ f⁎ h‖ 2 d v g for any smooth map f: M→ N, where d v g is the volume form on (M, g), and‖ f⁎ h‖ denotes the norm of the pullback f⁎ h of the metric h by the map f. We study stationary maps for the functional Φ (f), and show that stable stationary maps from or into minimal submanifolds in the unit spheres are rare if Ricci curvatures of submanifolds are large. Symmetric spaces of some type, which are minimally and isometrically immersed in the unit spheres, are treated in detail.
