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Stress energy tensor for symphonic maps

  • Nobumitsu Nakauchi
Article
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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.

Keywords

Variational problem Pullbacks of metrics Symphonic map 

Mathematics Subject Classification

Primary Secondary 58E99 58E20 53C43 

Notes

Acknowledgements

This work was partially supported by the Grant-in-Aid for Scientific Research (C) no. 18K03280 at Japan Society for the Promotion of Science.

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Copyright information

© Unione Matematica Italiana 2018

Authors and Affiliations

  1. 1.Graduate School of Sciences and Technology for InnovationYamaguchi UniversityYamaguchiJapan

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