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Some Kind of Stabilities and Instabilities of Energies of Maps Between Kähler Manifolds

  • Tetsuya Taniguchi
  • Seiichi Udagawa
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 111)

Abstract

We treat the variational problem of the energy of the map between two Riemannian manifolds. It is known that any holomorphic or anti-holomorphic map f: M → N between compact Kähler manifolds is stable for the variation f t of f with fixed Kähler metrics compatible with the holomorphic structures. Is this also stable for the variation g t of the metric g of M with fixed volume of M and fixed isometric map f? In this paper, we show that the answer is no if the dimension of M is no less than 3. This paper is a expositary note of Taniguchi and Udagawa (Characterizations of Ricci flat metrics and Lagrangian submanifolds in terms of the variational problem. To appear in Glasgow Math. J).

Keywords

Riemannian Manifold Variational Problem Variational Formula Riemannian Metrics Lagrangian Submanifolds 
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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.College of Liberal Arts and SciencesKitasato UniversitySagamiharaJapan

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