Dirac operators on Lagrangian submanifolds

Details Dirac operators on Lagrangian submanifolds Dirac operators on Lagrangian submanifolds

2004-05-14

arxiv.org/abs/math/0405270v1

Mathematics

Differential Geometry

16 pages; to appear in J. Geom. Phys

Scientific paper

10.1016/j.geomphys.2004.04.008

We study a natural Dirac operator on a Lagrangian submanifold of a K\"ahler
manifold. We first show that its square coincides with the Hodge-de Rham
Laplacian provided the complex structure identifies the Spin structures of the
tangent and normal bundles of the submanifold. We then give extrinsic estimates
for the eigenvalues of that operator and discuss some examples.

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