Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Generic vanishing for harmonic
spinors of twisted Dirac operators


Author: Nicolae Anghel
Journal: Proc. Amer. Math. Soc. 124 (1996), 3555-3561
MSC (1991): Primary 58G25; Secondary 47A53, 53C05
DOI: https://doi.org/10.1090/S0002-9939-96-03475-2
MathSciNet review: 1343678
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we address the problem of generic vanishing for (negative) harmonic spinors of Dirac operators coupled with variable metric connections.


References [Enhancements On Off] (What's this?)

  • [AS] M. Atiyah, I. M. Singer, The Index of Elliptic Operators on Compact Manifolds, Bull. Amer. Math. Soc. 69 (1963), 422-433. MR 26:626
  • [BW] B. Booß-Bavnbek, K. Wojciechowski, Elliptic Boundary Problems for Dirac Operators, Birkhäuser, Boston Basel Berlin, 1993. MR 94h:58168
  • [CM] A. Connes, H. Moscovici, The $L^{2}$-Index Theorem for Homogeneous Spaces of Lie Groups, Ann. Math. 115 (1982), 291-330. MR 84f:58108
  • [G] S. Goldberg, Unbounded Linear Operators, Theory and Applications, Dover Publications, Inc., New York, 1985. MR 86k:47001
  • [GL] M. Gromov, H. B. Lawson, Jr., Positive Scalar Curvature and the Dirac Operator on Complete Riemannian Manifolds, Publ. Math. IHES 58 (1983), 295-408. MR 85g:58082
  • [L] A. Lichnerowicz, Spineurs Harmoniques, C. R. Acad. Sci. Paris, Ser. A-B 257 (1963), 7-9. MR 27:6218
  • [LM] H. B. Lawson Jr., M.-L. Michelsohn, Spin Geometry, Princeton Univ. Press, Princeton, NJ, 1989. MR 91g:53001
  • [RS] M. Reed, B. Simon, Methods of Modern Mathematical Physics. Vol. II: Fourier Analysis, Self-Adjointness, Academic Press, New York San Francisco London, 1975. MR 58:12429b
  • [S] I. M. Singer, Families of Dirac Operators with Applications in Physics, Élie Cartan et les Mathématiques d'Aujourd'hui, Astérisque, Soc. Math. France, Paris, 1985, pp. 323-340. MR 88a:58192

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58G25, 47A53, 53C05

Retrieve articles in all journals with MSC (1991): 58G25, 47A53, 53C05


Additional Information

Nicolae Anghel
Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
Email: anghel@sol.acs.unt.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03475-2
Keywords: Spin manifold, Dirac operator, metric connection, harmonic spinor, generic vanishing
Received by editor(s): May 9, 1995
Additional Notes: Research supported in part by the Texas Advanced Research Program under Grant No. 003594-071.
Communicated by: Peter Li
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society