SPINc GEOMETRY OF KAHLER MANIFOLDS AND THE HODGE LAPLACIAN ON MINIMAL

Description

Niveau: Supérieur, Doctorat, Bac+8
SPINc GEOMETRY OF KAHLER MANIFOLDS AND THE HODGE LAPLACIAN ON MINIMAL LAGRANGIAN SUBMANIFOLDS O. HIJAZI, S. MONTIEL, AND F. URBANO Abstract. From the existence of parallel spinor fields on Calabi- Yau, hyper-Kahler or complex flat manifolds, we deduce the ex- istence of harmonic differential forms of different degrees on their minimal Lagrangian submanifolds. In particular, when the sub- manifolds are compact, we obtain sharp estimates on their Betti numbers. When the ambient manifold is Kahler-Einstein with pos- itive scalar curvature, and especially if it is a complex contact manifold or the complex projective space, we prove the existence of Kahlerian Killing spinor fields for some particular spinc struc- tures. Using these fields, we construct eigenforms for the Hodge Laplacian on certain minimal Lagrangian submanifolds and give some estimates for their spectra. Applications on the Morse index of minimal Lagrangian submanifolds are obtained. 1. Introduction Recently, connections between the spectrum of the classical Dirac operator on submanifolds of a spin Riemannian manifold and its ge- ometry were investigated. Even when the submanifold is spin, many problems appear. In fact, it is known that the restriction of the spin bundle of a spin manifoldM to a spin submanifold is a Hermitian bun- dle given by the tensorial product of the intrinsic spin bundle of the submanifold and certain bundle associated with the normal bundle of the immersion ([2, 3, 6]).

• vector bundles


• dirac operator


• spin bundle


• trivial spin


• kahler manifold should


• parallel spinor


• bundle associated


• manifold


• complex manifolds

Sujets

• Vector bundle
• Dirac operator
• Spinor bundle
• Manifold
• Complex manifold

Informations

• Publié par: profil-zyak-2012
• Nombre de lectures: 9
• Langue: English

Extrait

INSTITUT NATIONAL DE LA STATISTIQUE ET DES ETUDES ECONOMIQUES
Série des Documents de Travail du CREST
(Centre de Recherche en Economie et Statistique)








n° 2005-24

Econometrics of Individual
Labor Market Transitions

1D. FOUGERE
2T. KAMIONKA




























Les documents de travail ne reflètent pas la position de l'INSEE et n'engagent que
leurs auteurs.

Working papers do not reflect the position of INSEE but only the views of the authors.

1 CNRS and CREST-INSEE, CEPR and IZA. [e-mail]
2nd CREST-INSEE, Paris. [e-mail] ECONOMETRICS
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