Stress energy tensor for symphonic maps
- 15 Downloads
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.
KeywordsVariational problem Pullbacks of metrics Symphonic map
Mathematics Subject ClassificationPrimary Secondary 58E99 58E20 53C43
This work was partially supported by the Grant-in-Aid for Scientific Research (C) no. 18K03280 at Japan Society for the Promotion of Science.
- 1.Baird, P., Eells, J.: A conservation law for harmonic maps. In: Geometry Symposium Utrecht 1980, Lecture Note in Math, vol. 894, pp. 1–25. Springer (1981)Google Scholar