Hermitian Geometry and Complex Space-Time

  title={Hermitian Geometry and Complex Space-Time},
  author={Ali H. Chamseddine},
  journal={Communications in Mathematical Physics},
  • A. Chamseddine
  • Published 5 March 2005
  • Mathematics
  • Communications in Mathematical Physics
We consider a complex Hermitian manifold of complex dimensions four with a Hermitian metric and a Chern connection. It is shown that the action that determines the dynamics of the metric is unique, provided that the linearized Einstein action coupled to an antisymmetric tensor is obtained, in the limit when the imaginary coordinates vanish. The unique action is of the Chern-Simons type when expressed in terms of the Kähler form. The antisymmetric tensor field has gauge transformations coming… 

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