Vanishing Theorems and String Backgrounds

Details Vanishing Theorems and String Backgrounds Vanishing Theorems and String Backgrounds

2000-10-03

arxiv.org/abs/math/0010038v1

Class.Quant.Grav.18:1089-1110,2001

Mathematics

Differential Geometry

25 pages, Latex

Scientific paper

10.1088/0264-9381/18/6/309

We show various vanishing theorems for the cohomology groups of compact hermitian manifolds for which the Bismut connection has (restricted) holonomy contained in SU(n) and classify all such manifolds of dimension four. In this way we provide necessary conditions for the existence of such structures on hermitian manifolds. Then we apply our results to solutions of the string equations and show that such solutions admit various cohomological restrictions like for example that under certain natural assumptions the plurigenera vanish. We also find that under some assumptions the string equations are equivalent to the condition that a certain vector is parallel with respect to the Bismut connection.

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