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2012•The Pure and Applied MathematicsOpen access

A NOTE ON SPECIAL LAGRANGIANS OF COTANGENT BUNDLES OF SPHERES

Jae-Hyouk Lee

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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.

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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.

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Available 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.

Key concepts: Submanifold, Cotangent bundle, Lagrangian, SPHERES, Mathematics, Normal bundle, Pure mathematics, Bundle

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