Browsing by Author "Moroianu, Andrei"

Now showing 1 - 6 of 6
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    Generalized killing spinors and Lagrangian graphs
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2014) Moroianu, Andrei; Semmelmann, Uwe
    We 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.
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    Generalized Vector Cross Products and Killing Forms on Negatively Curved Manifolds
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2018) Barberis, María Laura; Moroianu, Andrei; Semmelmann, Uwe
    Motivated by the study of Killing forms on compact Riemannian manifolds of negative sectional curvature, we introduce the notion of generalized vector cross products on Rⁿ and give their classification. Using previous results about Killing tensors on negatively curved manifolds and a new characterization of SU(3)-structures in dimension 6 whose associated 3-form is Killing, we then show that every Killing 3-form on a compact n-dimensional Riemannian manifold with negative sectional curvature vanishes if n≥4.
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    Invariant four-forms and symmetric pairs
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2012) Moroianu, Andrei; Semmelmann, Uwe
    We 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.
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    Killing tensors on tori
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Heil, Konstantin; Moroianu, Andrei; Semmelmann, Uwe
    We 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.
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    Metric Connections with Parallel Skew-Symmetric Torsion
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2018) Cleyton, Richard; Moroianu, Andrei; Semmelmann, Uwe
    A geometry with parallel skew-symmetric torsion is a Riemannian manifold carrying a metric connection with parallel skew-symmetric torsion. Besides the trivial case of the Levi-Civita connection, geometries with non-vanishing parallel skew-symmetric torsion arise naturally in several geometric contexts, e.g. on naturally reductive homogeneous spaces, nearly Kähler or nearly parallel G2-manifolds, Sasakian and 3-Sasakian manifolds, or twistor spaces over quaternion-Kähler manifolds with positive scalar curvature. In this paper we study the local structure of Riemannian manifolds carrying a metric connection with parallel skew-symmetric torsion. On every such manifold one can define a natural splitting of the tangent bundle which gives rise to a Riemannian submersion over a geometry with parallel skew-symmetric torsion of smaller dimension endowed with some extra structure. We show how previously known examples of geometries with parallel skew-symmetric torsion fit into this pattern, and construct several new examples. In the particular case where the above Riemannian submersion has the structure of a principal bundle, we give the complete local classification of the corresponding geometries with parallel skew-symmetric torsion.
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    Weakly complex homogeneous spaces
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2012) Moroianu, Andrei; Semmelmann, Uwe
    We 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.