Dirac operators on Lagrangian submanifolds
نویسنده
چکیده
We study a natural Dirac operator on a Lagrangian submanifold of a Kähler 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. Mathematics Subject Classification: 53C15, 53C27, 53C40
منابع مشابه
Isotropic Lagrangian Submanifolds in Complex Space Forms
In this paper we study isotropic Lagrangian submanifolds , in complex space forms . It is shown that they are either totally geodesic or minimal in the complex projective space , if . When , they are either totally geodesic or minimal in . We also give a classification of semi-parallel Lagrangian H-umbilical submanifolds.
متن کاملDirac reduction revisited
The procedure of Dirac reduction of Poisson operators on submanifolds is discussed within a particularly useful special realization of the general Marsden-Ratiu reduction procedure. The Dirac classification of constraints on ’first-class’ constraints and ’second-class’ constraints is reexamined. AMS 2000 Subject Classification: 70H45, 53D17, 70G45
متن کاملBiharmonic Capacity and the Stability of Minimal Lagrangian Submanifolds
We study the eigenvalues of the biharmonic operators and the buckling eigenvalue on complete, open Riemannian manifolds. We show that the first eigenvalue of the biharmonic operator on a complete, parabolic Riemannian manifold is zero. We give a generalization of the buckling eigenvalue and give applications to studying the stability of minimal Lagrangian submanifolds in Kähler manifolds. MSC 1...
متن کاملDirac Operators, Conformal Transformations and Aspects of Classical Harmonic Analysis
The main thrust of this paper is to investigate the intimate link between the conformal group and singular integral operators, in particular, but not exclusively, operators of Calderón–Zygmund type, together with associated commutators acting on the L spaces of surfaces. Clifford analysis and Dirac operators are the basic tools used to help to unify these themes. These surfaces lie in euclidean...
متن کامل0 Submanifold Differential Operators in D - Module Theory II
This article is one of a series of papers. For this decade, the Dirac operator on a submanifold has been studied as a restriction of the Dirac operator in n-dimensional euclidean space E n to a surface or a space curve as physical models. These Dirac operators are identified with operators of the Frenet-Serret relation for a space curve case and of the generalized Weierstrass relation for a con...
متن کامل