Christof Puhle

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Let (M, g) be a Riemannian spin manifold. The basic equations in supergravity models of type IIa string theory with 4-form flux involve a 3-form T , a 4-form F , a spinorial covariant derivative ∇ depending on ∇, T , F , and a ∇-parallel spinor field Ψ. We classify and construct many explicit families of solutions to this system of spinorial field equations(More)
Any Spin (7)-manifold admits a metric connection ∇ with totally skewsymmetric torsion T preserving the underlying structure. We classify those with ∇-parallel T 6= 0 and non-Abelian isotropy algebra iso (T) 6 spin (7). These are isometric to either Riemannian products or homogeneous naturally reductive spaces, each admitting two ∇-parallel spinor fields.
In [3] the authors studied the 4-parameter family of isospectral flat 4-tori T ± (a, b, c, d) discovered by Conway and Sloane. With a particular method of counting nodal domains they were able to distinguish these tori (numerically) by computing the corresponding nodal sequences relative to a few explicit tuples (a, b, c, d). In this note we confirm the(More)
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