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http://dx.doi.org/10.7468/jksmeb.2012.19.3.239

A NOTE ON SPECIAL LAGRANGIANS OF COTANGENT BUNDLES OF SPHERES

Lee, Jae-Hyouk (Department of Mathematics, Ewha Womans University)

Publication Information

The Pure and Applied Mathematics / v.19, no.3, 2012 , pp. 239-249 More about this Journal

Abstract

For each submanifold X in the sphere $S^n$ ; we show that the corresponding conormal bundle $N^*X$ is Lagrangian for the Stenzel form on $T^*S^n$ . Furthermore, we correspond an austere submanifold X to a special Lagrangian submanifold $N^*X$ in $T^*S^n$ . We also discuss austere submanifolds in $S^n$ from isoparametric geometry.

Keywords

special Lagrangians; cotangent bundle; Stenzel metric;

Citations & Related Records

Reference

1	U. Abresch: Isoparametric hypersurfaces with four or six distinct principal curvatures. Necessary conditions on the multiplicities. Math. Ann. 264 (1983), no. 3, 283-302. DOI
2	H. Anciaux: Special Lagrangian submanifolds in the complex sphere. Ann. Fac. Sci. Toulouse Math. (6) 16 (2007), no. 2, 215-227. DOI
3	V. Borrelli & C. Gorodski: Minimal Legendrian submanifolds of $S^{2n+1}$ and absolutely area-minimizing cones. Differential Geom. Appl. 21 (2004), no. 3, 337-347. DOI
4	E. Calabi: Meriques Kahleriennes et fibres holomorphes. Ann. Ec. Norm. Sup. 12 (1979), 269-294. DOI
5	J. Dorfmeister & E. Neher: Isoparametric hypersurfaces, case g=6,m=1. Comm. Algebra 13 (1985), no. 11, 2299-2368. DOI
6	R. Harvey & B. Lawson: Calibrated geometries. Acta Math. 148 (1982), 47-157. DOI
7	W. Hsiang & B. Lawson: Minimal submanifolds of low cohomogeneity. J. Differential Geometry 5 (1971), 1-38. DOI
8	N. Hitchin: Hyperkahler manifolds. Seminaire Bourbaki, Asterisque 206(1992) 137-166.
9	M. Ionel & M. Min-Oo: Cohomogeneity One Special Lagrangian Submanifolds in the Deformed Conifold. [math/0504557]
10	M. Kimura: A generalization of Cartan hypersurfaces. Proceedings of the Ninth International Workshop on Differential Geometry, 51-59, Kyungpook Nat'l. Univ., Taegu, 2005.
11	S. Karigiannis & M. Min-Oo: Calibrated subbundles in noncompact manifolds of special holonomy. Ann. Global Anal. Geom. 28 (2005), no. 4, 371-394. DOI
12	J.H. Lee: Special Lagragnian Submanifolds in Cotangent Bundles. On progresss.
13	R. Miyaoka: A new proof of the homogeneity of isoparametric hypersurfaces with (g;m) = (6; 1). Geometry and topology of submanifolds, X (Beijing/Berlin, 1999), 178-199, World Sci. Publ., River Edge, NJ, 2000.
14	M.B. Stenzel: Ricci-flat metrics on the complexi¯cation of a compact rank one symmetric space. Manuscripta Math. 80 (1993), no. 2, 151-163. DOI
15	R. Szoke: Complex structures on tangent bundles of Riemannian manifolds. Math. Ann. 291 (1991), 409-428. DOI