Embedding into manifolds with torsion

Details Embedding into manifolds with torsion Embedding into manifolds with torsion

2008-12-22

arxiv.org/abs/0812.4186v2

Math. Z. (2011) 268:725-751

Mathematics

Differential Geometry

24 pages; v2: added new example concerning the group PSU(3); typos corrected; improved presentation

Scientific paper

10.1007/s00209-010-0692-7

We introduce a class of special geometries associated to the choice of a differential graded algebra contained in \Lambda R^n. We generalize some known embedding results, that effectively characterize the real analytic Riemannian manifolds that can be realized as submanifolds of a Riemannian manifold with special holonomy, to this more general context. In particular, we consider the case of hypersurfaces inside nearly-Kaehler and alpha-Einstein-Sasaki manifolds, proving that the corresponding evolution equations always admit a solution in the real analytic case.

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