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Eigenvalue Estimates of the spinc Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Eigenvalue Estimates of the spinc Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds
Інший ID:
2010 Mathematics Subject Classification: 53C27; 53C25; 53C55; 58J50; 83C60
DOI:10.3842/SIGMA.2015.054
DOI:10.3842/SIGMA.2015.054
Посилання:
Eigenvalue Estimates of the spinc Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds / R. Nakad, M. Pilca // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 39 назв. — англ.
Підтримка:
The first named author gratefully acknowledges the financial support of the Berlin Mathematical
School (BMS) and would like to thank the University of Potsdam, especially Christian B¨ar and
his group, for their generous support and friendly welcome during summer 2013 and summer
2014. The first named author thanks also the Faculty of Mathematics of the University of
Regensburg for its support and hospitality during his two visits in July 2013 and July 2014.
The authors are very much indebted to Oussama Hijazi and Andrei Moroianu for many useful
discussions. Both authors thank the editor and the referees for carefully reading the paper and
for providing constructive comments, which substantially improved it.
Дата:
2015
Переглядів:
465
Завантажень:
237
Анотація:
We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact Kähler-Einstein manifold of positive scalar curvature and endowed with particular spinc structures. The limiting case is characterized by the existence of Kählerian Killing spinc spinors in a certain subbundle of the spinor bundle. Moreover, we show that the Clifford multiplication between an effective harmonic form and a Kählerian Killing spinc spinor field vanishes. This extends to the spinc case the result of A. Moroianu stating that, on a compact Kähler-Einstein manifold of complex dimension 4ℓ+3 carrying a complex contact structure, the Clifford multiplication between an effective harmonic form and a Kählerian Killing spinor is zero.
