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- ItemGeneralized killing spinors and Lagrangian graphs(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2014) Moroianu, Andrei; Semmelmann, UweWe study generalized Killing spinors on the standard sphere S3, which turn out to be related to Lagrangian embeddings in the nearly Kähler manifold S3×S3 and to great circle flows on S3. Using our methods we generalize a well known result of Gluck and Gu [6] concerning divergence-free geodesic vector fields on the sphere and we show that the space of Lagrangian submanifolds of S3×S3 has at least three connected components.
- ItemWeakly complex homogeneous spaces(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2012) Moroianu, Andrei; Semmelmann, UweWe complete our recent classification [GMS11] of compact inner symmetric spaces with weakly complex tangent bundle by filling up a case which was left open, and extend this classification to the larger category of compact homogeneous spaces with positive Euler characteristic. We show that a simply connected compact equal rank homogeneous space has weakly complex tangent bundle if and only if it is a product of compact equal rank homogeneous spaces which either carry an invariant almost complex structure (and are classified by Hermann [H56]), or have stably trivial tangent bundle (and are classified by Singhof and Wemmer [SW86]), or belong to an explicit list of weakly complex spaces which have neither stably trivial tangent bundle, nor carry invariant almost complex structures.
- ItemKilling tensors on tori(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Heil, Konstantin; Moroianu, Andrei; Semmelmann, UweWe show that Killing tensors on conformally at n-dimensional tori whose con- formal factor only depends on one variable, are polynomials in the metric and in the Killing vector elds. In other words, every rst integral of the geodesic ow polynomial in the momenta on the sphere bundle of such a torus is linear in the momenta.
- ItemInvariant four-forms and symmetric pairs(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2012) Moroianu, Andrei; Semmelmann, UweWe give criteria for real, complex and quaternionic representations to define s-representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of complex representations whose second exterior power is irreducible or has an irreducible summand of co-dimension one, and we give a conceptual computation-free argument for the construction of the exceptional Lie algebras of compact type.