Abstract
We consider a functional of pullbacks of metrics on the space of maps between Riemannian manifolds. Stationary maps for this functional are called symphonic maps (Kawai and Nakauchi in Nonlinear Anal 74:2284–2295, 2011; Differ Geom Appl 44:161–177, 2016; Misawa and Nakauchi in Nonlinear Anal 75:5971–5974, 2012; Calc Var Partial Differ Equ 55:1–20, 2016; Adv Differ Equ, 2018; Nakauchi and Takakuwa in Nonlinear Anal 108:87–98, 2014; Nakauchi and Takenaka in Ricerche di Matematica 60:219–235, 2011). In this paper we introduce a stress energy tensor for symphonic maps and give some results.
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