On the spectrum of the twisted Dolbeault Laplacian over Kähler manifolds

DOI10.1016/j.difgeo.2008.10.018zbMath1173.58012arXiv0706.0878OpenAlexW2616458583WikidataQ115357365 ScholiaQ115357365MaRDI QIDQ1023415

Rafael F. Leão, Marcos Jardim

Publication date: 11 June 2009

Published in: Differential Geometry and its Applications, Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.0878

zbMATH Keywords

geometryholomorphic vector bundleYang-Mills theoryeigenvalues and eigenfunctionstwisted Dolbeault LaplacianHermitian connectionvectorsmathematical operators

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spin and Spin({}^c) geometry (53C27) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items

A note on twisted Dirac operators on closed surfaces ⋮ On the space of connections having non-trivial twisted harmonic spinors ⋮ \((1,1)\)-forms acting on spinors on Kähler surfaces ⋮ Bicomplex linear operators on bicomplex Hilbert spaces and Littlewood's subordination theorem ⋮ On the spectrum of the twisted Dolbeault Laplacian over Kähler manifolds

Cites Work

• The first eigenvalue of the Dirac operator on Kähler manifolds
• On the spectrum of the twisted Dolbeault Laplacian over Kähler manifolds
• An estimation for the first eigenvalue of the Dirac operator on closed Kähler manifolds of positive scalar curvature
• Eigenvalue estimates for the Dirac operator on quaternionic Kähler manifolds
• The first eigenvalue of the Dirac operator on quaternionic Kähler manifolds
• Upper bound for the first eigenvalue of algebraic submanifolds
• Curvature dependent lower bounds for the first eigenvalue of the Dirac operator
• Harmonic spinors
• Eigenvalue estimates for Dirac operators coupled to instantons
• Holomorphic spectral geometry of magnetic Schrödinger operators on Riemann surfaces
• Holomorphic spectrum of twisted Dirac operators on compact Riemann surfaces
• Spectral asymmetry and Riemannian geometry. III
• The spectrum of twisted Dirac operators on compact flat manifolds
• Eigenvalues of the Laplacian acting on 𝑝-forms and metric conformal deformations
• The Dolbeault operator on Hermitian spin surfaces
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