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This work was written while the author was visiting IHES during the academic, year 1987–1988
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Bismut, JM. A local index theorem for non Kähler manifolds. Math. Ann. 284, 681–699 (1989). https://doi.org/10.1007/BF01443359
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DOI: https://doi.org/10.1007/BF01443359