Spinc geometry of Kähler manifolds and the Hodge Laplacian on minimal Lagrangian submanifolds

Autor:	Sebasti n Montiel, Oussama Hijazi, Francisco Urbano
Rok vydání:	2006
Předmět:	Spinor Betti number General Mathematics Complex projective space Geometry Dirac operator Manifold symbols.namesake Killing spinor symbols Mathematics::Differential Geometry Mathematics::Symplectic Geometry Laplace operator Scalar curvature Mathematics
Zdroj:	Mathematische Zeitschrift. 253:821-853
ISSN:	1432-1823 0025-5874
DOI:	10.1007/s00209-006-0936-8
Popis:	From the existence of parallel spinor fields on Calabi-Yau, hyper-Kahler 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 which generalize those obtained by Smoczyk in [49]. When the ambient manifold is Kahler-Einstein with positive 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 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. These results also generalize some theorems by Smoczyk in [50]. Finally, applications on the Morse index of minimal Lagrangian submanifolds are obtained.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d2b68b6b8f524892e509e390c2a67f76 https://doi.org/10.1007/s00209-006-0936-8 Zobrazit plný text záznamu Full text from SpringerLink