## Tohoku Mathematical Journal 2012 March SECOND SERIES VOL. 64, NO. 1

 Tohoku Math. J. 64 (2012), 141-169

Title COHOMOGENEITY ONE SPECIAL LAGRANGIAN SUBMANIFOLDS IN THE COTANGENT BUNDLE OF THE SPHERE

Author Kaname Hashimoto and Takashi Sakai

(Received February 24, 2011, revised August 5, 2011)
Abstract. We classify cohomogeneity one special Lagrangian submanifolds in the cotangent bundle of the sphere $S^n$ invariant under $SO(p) \times SO(n+1-p)$ with respect to the Stenzel metric and a Ricci-flat cone Kähler metric. Moreover, we describe the asymptotic behavior and singularities of such special Lagrangian submanifolds.

2000 Mathematics Subject Classification. Primary 53C38.

Key words and phrases. Special Lagrangian submanifold, Calabi-Yau manifold, calibration, minimal submanifold.