## The Michigan Mathematical Journal

### Second variation of compact minimal Legendrian submanifolds of the sphere

Francisco Urbano

#### Article information

Source
Michigan Math. J., Volume 51, Issue 2 (2003), 437-447.

Dates
First available in Project Euclid: 4 August 2003

https://projecteuclid.org/euclid.mmj/1060013206

Digital Object Identifier
doi:10.1307/mmj/1060013206

Mathematical Reviews number (MathSciNet)
MR1992956

Zentralblatt MATH identifier
1043.53052

#### Citation

Urbano, Francisco. Second variation of compact minimal Legendrian submanifolds of the sphere. Michigan Math. J. 51 (2003), no. 2, 437--447. doi:10.1307/mmj/1060013206. https://projecteuclid.org/euclid.mmj/1060013206

#### References

• N. Ejiri, Totally real minimal immersions of $n$-dimensional real space forms into $n$-dimensional complex space forms, Proc. Amer. Math. Soc. 84 (1982), 243--246.
• ------, The index of minimal immersions of $\Bbb S^2$ into $\Bbb S^2n,$ Math. Z. 184 (1983), 127--132.
• A. El Soufi and S. Ilias, Riemannian manifolds admitting isometric immersions by their first eigenfunctions, Pacific J. Math. 195 (2000), 91--99.
• A. Ikeda and Y. Taniguchi, Spectra and eigenforms of the Laplacian on $\Bbb S^n$ and $\Bbb P^n(\Bbb C),$ Osaka J. Math. 15 (1978), 515--546.
• D. Joyce, Lectures on Calabi--Yau and special Lagrangian geometry, math.DG/0108088 (2001).
• H. Lê and G. Wang, A characterization of minimal Legendrian submanifolds in $\Bbb S^2n+1,$ Compositio Math. 129 (2001), 87--93.
• S. Montiel and F. Urbano, Second variation of superminimal surfaces into self-dual Einstein four-manifolds, Trans. Amer. Math. Soc. 349 (1997), 2253--2269.
• M. Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan 14 (1962), 333--340.
• Y. G. Oh, Second variation and stabilities of minimal Lagrangian submanifolds in Kähler manifolds, Invent. Math. 101 (1990), 501--519.
• A. Ros, Spectral geometry of CR-minimal submanifolds in the complex projective space, Kodai Math. J. 6 (1983), 88--99.
• J. Simons, Minimal varieties in Riemannian manifolds, Ann. of Math. (2) 88 (1968), 62--105.
• F. Urbano, Minimal surfaces with low index in the three-dimensional sphere, Proc. Amer. Math. Soc. 108 (1990), 989--992.
• ------, Index of Lagrangian submanifolds of $\Bbb C\Bbb P^n$ and the laplacian of $1$-forms, Geom. Dedicata 48 (1993), 309--318.
• S. T. Yau, Submanifolds with constant mean curvature, I, Amer. J. Math. 96 (1974), 346--366.