ACTA issues

Local index theorem for the modified Dirac operator

S. L. Yang

Acta Sci. Math. (Szeged) 71:1-2(2005), 391-404

Abstract. The Dirac operators are important differential operators. Bismut got a local index theorem for the modified Dirac operators over the Spin manifolds. In this paper, we obtained a similar theorem over the Spin$^c$-manifolds and used the heat equation to prove this theorem.

AMS Subject Classification (1991): 53C27

Keyword(s): ^c, spin-manifold, Dirac operator, local index, MP Parametrix, Chern root

Received March 18, 2004, and in revised form April 16, 2005. (Registered under 5876/2009.)