Spin$^c$ geometry of Kähler manifolds and the Hodge Laplacian on minimal Lagrangian submanifolds

From the existence of parallel spinor fields on Calabi-Yau, hyper-Kähler or complex flat manifolds, we deduce the existence of harmonic differential forms of different degrees on their minimal Lagrangian submanifolds. In particular, when the submanifolds are compact, we obtain sharp estimates on the...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Mathematische Zeitschrift Ročník 253, Number 4; s. 821 - 853
Hlavní autoři: Hijazi, Oussama, Montiel, S., Urbano, F.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Springer 2006
Témata:
Differential Geometry
Mathematics
Hodge Laplacian
Spin$^c$ geometry
Lagrangian submanifolds
Dirac operator
ISSN:0025-5874, 1432-1823
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:From the existence of parallel spinor fields on Calabi-Yau, hyper-Kähler or complex flat manifolds, we deduce the existence of harmonic differential forms of different degrees on their minimal Lagrangian submanifolds. In particular, when the submanifolds are compact, we obtain sharp estimates on their Betti numbers. When the ambient manifold is Kähler-Einstein with positive scalar curvature, and especially if it is a complex contact manifold or the complex projective space, we prove the existence of Kählerian Killing spinor fields for some particular spin$^c$ structures. 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.
ISSN:0025-5874
1432-1823