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December 2012 The second variational formula of the $k$-energy and $k$-harmonic curves
Shun Maeta
Osaka J. Math. 49(4): 1035-1063 (December 2012).

Abstract

In [4], J. Eells and L. Lemaire introduced $k$-energy and $k$-harmonic maps. In 1989, S.B. Wang [17] showed the first variation formula of the $k$-energy. In this paper, we give the second variation formula of $k$-energy and a notion of weakly stable and unstable. We also study $k$-harmonic maps into product Riemannian manifolds and $k$-harmonic curves into Riemannian manifolds with constant sectional curvature. Moreover, we give some non-trivial solutions of $3$-harmonic curves.

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Shun Maeta. "The second variational formula of the $k$-energy and $k$-harmonic curves." Osaka J. Math. 49 (4) 1035 - 1063, December 2012.

Information

Published: December 2012
First available in Project Euclid: 19 December 2012

zbMATH: 1273.58008
MathSciNet: MR3007953

Subjects:
Primary: 58E20
Secondary: 53C43

Rights: Copyright © 2012 Osaka University and Osaka City University, Departments of Mathematics

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Vol.49 • No. 4 • December 2012
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