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Killing spinor equations in dimension 7 and geometry of integrable G2-manifolds

2003; Elsevier BV; Volume: 48; Issue: 1 Linguagem: Inglês

10.1016/s0393-0440(03)00005-6

1879-1662

Thomas Friedrich, Stefan Ivanov,

Geometric Analysis and Curvature Flows

We compute the scalar curvature of seven-dimensional G2-manifolds admitting a G2-connection with totally skew-symmetric torsion. We prove the formula for the general solution of the Killing spinor equation and express the Riemannian scalar curvature of the solution in terms of the dilation function and the NS 3-form field. In dimension n=7 the dilation function involved in the second fermionic string equation has an interpretation as a conformal change of the underlying integrable G2-structure into a cocalibrated one of pure type W3.