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Toru kajigaya （Tohoku Univ.、King's College London） |
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| Title : On the minimality of normal bundles and austere submanifolds |
Abstract
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The notion of austere submanifolds in a Riemannian manifold was first
introduced by Harvey and Lawson to construct special Lagrangian submanifolds
in the complex Euclidean space C^n. They proved that a submanifold in the
Euclidean space R^n is austere if and only if the normal bundle is special
Lagrangian in the tangent bundle over R^n which is naturally regarded as
C^n. However, the geometrical interpretation of austere submanifolds in
general Riemannian manifolds is unknown except a few cases. In this talk,
we generalize their result as a context of minimal normal bundles in tangent
bundles equipped with Sasaki metric, and give a characterization of austere
submanifolds in the real space forms. Moreover, we investigate extrinsic
properties of Lagrangian normal bundles. In particular, we discuss the
minimality of normal bundles in the tangent bundles over the complex space
forms, and the Hamiltonian minimality of normal bundles over isoparametric
submanifolds in R^n.
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Organizer: Reiko Miyaoka
Contact：
Grants-in-Aids for Scientific research：23340012 |
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