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arxiv: math/0112201 · v1 · pith:33YIASD3new · submitted 2001-12-19 · 🧮 math.DG · hep-th

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

Thomas Friedrich (Berlin) , Stefan Ivanov (Sofia) This is my paper
classification 🧮 math.DG hep-th
keywords curvaturedilationdimensionequationfunctionintegrablekillingmanifolds
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We compute the scalar curvature of 7-dimensional ${G}_2$-manifolds admitting a 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 ${G}_2$-structure into a cocalibrated one of pure type $W_3$.

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  1. On the rigidity of special and exceptional geometries with torsion a closed $3$-form

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    Riemannian manifolds with a closed parallel torsion 3-form are locally N × G (G semisimple), enabling simplified proofs and explicit classification of strong G2, Spin(7), and certain 8D HKT manifolds.