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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.)
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