Einstein warped \(\mathrm{G}_{2}\) and spin(7) manifolds. (English) Zbl 1417.53051
Summary: In this paper most of the classes of \(\mathrm{G}_{2}\)-structures with Einstein induced metric of negative, null, or positive scalar curvature are realized. This is carried out by means of warped \(\mathrm{G}_{2}\)-structures with fiber an Einstein SU(3) manifold. The torsion forms of any warped \(\mathrm{G}_{2}\)-structure are explicitly described in terms of the torsion forms of the SU(3)-structure and the warping function, which allows to give characterizations of the principal classes of Einstein warped \(\mathrm{G}_{2}\) manifolds. Similar results are obtained for Einstein warped Spin(7) manifolds with fiber a \(\mathrm{G}_{2}\) manifold.
Keywords:
null scalar curvature; positive scalar curvature; Einstein \(\operatorname{SU}(3)\) manifold; Einstein warped Spin(7) manifoldsReferences:
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