A spectral estimate for the Dirac operator on Riemannian flows

Nicolas Ginoux; Georges Habib

Open Mathematics (2010)

  • Volume: 8, Issue: 5, page 950-965
  • ISSN: 2391-5455

Abstract

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We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on both Sasakian and 3-dimensional manifolds, and partially classify those satisfying the limiting case. Finally, we compare our estimate with a lower bound in terms of a natural tensor depending on the eigenspinor.

How to cite

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Nicolas Ginoux, and Georges Habib. "A spectral estimate for the Dirac operator on Riemannian flows." Open Mathematics 8.5 (2010): 950-965. <http://eudml.org/doc/269726>.

@article{NicolasGinoux2010,
abstract = {We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on both Sasakian and 3-dimensional manifolds, and partially classify those satisfying the limiting case. Finally, we compare our estimate with a lower bound in terms of a natural tensor depending on the eigenspinor.},
author = {Nicolas Ginoux, Georges Habib},
journal = {Open Mathematics},
keywords = {Foliations; Sasakian manifolds; Spin geometry; Spectral geometry; Estimation of eigenvalues - upper and lower bounds; spectral estimates for the Dirac operator; Riemannian flows; Killing spinors},
language = {eng},
number = {5},
pages = {950-965},
title = {A spectral estimate for the Dirac operator on Riemannian flows},
url = {http://eudml.org/doc/269726},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Nicolas Ginoux
AU - Georges Habib
TI - A spectral estimate for the Dirac operator on Riemannian flows
JO - Open Mathematics
PY - 2010
VL - 8
IS - 5
SP - 950
EP - 965
AB - We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on both Sasakian and 3-dimensional manifolds, and partially classify those satisfying the limiting case. Finally, we compare our estimate with a lower bound in terms of a natural tensor depending on the eigenspinor.
LA - eng
KW - Foliations; Sasakian manifolds; Spin geometry; Spectral geometry; Estimation of eigenvalues - upper and lower bounds; spectral estimates for the Dirac operator; Riemannian flows; Killing spinors
UR - http://eudml.org/doc/269726
ER -

References

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