On the Dirac spectrum of Riemannian foliations admitting a basic parallel 1-form

DOI10.1016/j.geomphys.2012.01.004zbMath1253.53024OpenAlexW2012358091WikidataQ115353235 ScholiaQ115353235MaRDI QIDQ408230

Vladimir Slesar

Publication date: 29 March 2012

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2012.01.004

zbMATH Keywords

Riemannian foliationsbasic Dirac operatorWeitzenböck-Lichnerowicz formula

Mathematics Subject Classification ID

Spin and Spin({}^c) geometry (53C27) Foliations (differential geometric aspects) (53C12) Foliations in differential topology; geometric theory (57R30)

Related Items (2)

Seiberg-Witten invariants on manifolds with Riemannian foliations of codimension 4 ⋮ TRANSVERSAL KILLING AND TWISTOR SPINORS ASSOCIATED TO THE BASIC DIRAC OPERATORS

Cites Work

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• Eigenvalue estimates for the basic Dirac operator on a Riemannian foliation admitting a basic harmonic 1-form
• Vanishing theorem for transverse Dirac operators on Riemannian foliations
• Weitzenböck formulas for Riemannian foliations
• A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors
• De Rham-Hodge theory for Riemannian foliations
• Transversal Dirac families in Riemannian foliations
• An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold admitting parallel one-form
• Adiabatic limits and spectral sequences for Riemannian foliations
• The basic component of the mean curvature of Riemannian foliations
• Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length
• Foliated manifolds with bundle-like metrics
• A brief note on the spectrum of the basic Dirac operator
• Der erste Eigenwert des Dirac‐Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung
• The basic Laplacian of a Riemannian foliation
• The first eigenvalue of the transversal Dirac operator

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