Chinese Quarterly Journal of Mathematics ›› 2004, Vol. 19 ›› Issue (2): 120-125.

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Eigenvalues of Spinc Dirac Operator

  

  1.  College of Mathematics and Information Science, Henan University, Kaifeng 475001, China; Zhengzhou Teacher's College, Zhengzhou 450044, China; Department of Mathematics, Lanzhou University, Lanzhou 730000, China; Institute of Mathematics, Henan University, Kaifeng 475001, China
  • Received:2004-02-20 Online:2004-06-30 Published:2024-03-15
  • About author:FENG Xiu-fang(1965-),female,native of Changge,Henan,a lecturer of Henan University, M.S.D.,engages in partial differential equation;LAN She-yun(1956-),female,native of Zhengzhou,Henan,an advanced lecturer of Zhengzhou Teacher's College,engages in partial differential equation;DING Lu(1980-), female,native of Luohe,graduate student,engages in mathematics physics;ZHENG Zhu-jun(1966-),male, native of Changge,Henan,a professor of Henan University,Ph.D.,engages in partial differential equation, mathenatics physics.
  • Supported by:
     Supported in part by Mathematics Tianyuan Fund(10226002);

Abstract: In this paper we research the lower bound of the eigenvalue of Spinc Dirac operator on the Spinc manifold. By the Weisenbock formula, we get an estimate of it, then following the idea of Th Friedrich [2] and X Zhang [6]. We get a finer estimate of it. As an application, we give a condition when the Seiberg-Witten equation only has 0 solution.

Key words: eigenvalue;Spinc Dirac , operator;Seiberg-Witten , equation

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