The Michigan Mathematical Journal

Second variation of compact minimal Legendrian submanifolds of the sphere

Francisco Urbano

Full-text: Open access

Article information

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

First available in Project Euclid: 4 August 2003

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]


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.

Export citation


  • 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.