Search results for " 58C50"

showing 2 items of 2 documents

Supermanifolds, symplectic geometry and curvature

2015

We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.

Mathematics - Differential GeometryGeneral Relativity and Quantum CosmologyHigh Energy Physics::TheoryDifferential Geometry (math.DG)FOS: MathematicsFOS: Physical sciencesMathematics::Differential GeometryMathematical Physics (math-ph)58A50 58C50 53D35Mathematics::Symplectic GeometryMathematical Physics
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Quillen superconnections and connections on supermanifolds

2013

Given a supervector bundle $E = E_0\oplus E_1 \to M$, we exhibit a parametrization of Quillen superconnections on $E$ by graded connections on the Cartan-Koszul supermanifold $(M;\Omega (M))$. The relation between the curvatures of both kind of connections, and their associated Chern classes, is discussed in detail. In particular, we find that Chern classes for graded vector bundles on split supermanifolds can be computed through the associated Quillen superconnections.

Mathematics - Differential GeometryHigh Energy Physics - TheoryChern classGeneral Physics and AstronomyVector bundleFOS: Physical sciences53C07 58C50 81T13Mathematical Physics (math-ph)Mathematics::Algebraic TopologyAlgebraHigh Energy Physics::TheoryDifferential Geometry (math.DG)High Energy Physics - Theory (hep-th)Mathematics::K-Theory and HomologyBundleSupermanifoldFOS: MathematicsGeometry and TopologyMathematics::Differential GeometryParametrizationMathematics::Symplectic GeometryMathematical PhysicsMathematics
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