Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Constructing the Kähler and the symplectic structures from certain spinors on 4-manifolds


Authors: Y. Byun, Y. Lee, J. Park and J. S. Ryu
Journal: Proc. Amer. Math. Soc. 129 (2001), 1161-1168
MSC (1991): Primary 53C05, 53C07
Published electronically: September 20, 2000
MathSciNet review: 1707139
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract:

We show that, on an oriented Riemannian 4-manifold, existence of a non-zero parallel spinor with respect to a spin$^c$ structure implies that the underlying smooth manifold admits a Kähler structure. A similar but weaker condition is obtained for the 4-manifold to admit a symplectic structure. We also show that the $spin^c$ structure in which the non-zero parallel spinor lives is equivalent to the canonical spin$^c$ structure associated to the Kähler structure.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53C05, 53C07

Retrieve articles in all journals with MSC (1991): 53C05, 53C07


Additional Information

Y. Byun
Affiliation: Department of Mathematics, College of Natural Science, Hanyang University, Sungdong-gu, Seoul 133-791, Korea
Email: yhbyun@fermat.hanyang.ac.kr

Y. Lee
Affiliation: Department of Mathematics, College of Natural Science, Inha University, Incheon-si 402-751, Korea
Email: ywlee@math.inha.ac.kr

J. Park
Affiliation: Department of Mathematics, College of Natural Science, Dongguk University, Joong-gu, Seoul 100-715, Korea
Email: jpark@cakra.dongguk.ac.kr

J. S. Ryu
Affiliation: Department of Mathematics Education, College of Education, Hongik University, Mapo-gu, Seoul 121-791, Korea
Email: jsryu@math.hongik.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05587-8
PII: S 0002-9939(00)05587-8
Keywords: Parallel positive spinor, K\"{a}hler manifold, symplectic manifold, $spin^{c}$ structure
Received by editor(s): April 30, 1999
Received by editor(s) in revised form: June 21, 1999
Published electronically: September 20, 2000
Additional Notes: The first author was partially supported by the Hanyang University Research Fund. The second author was supported in part by 1998-015-D00044. The third author was partially supported by the Dongguk University Research Fund. The fourth author was supported in part by GARC
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society