Transitive Courant algebroids.

Vaisman, Izu

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Geometric structures on the tangent bundle of the Einstein spacetime

Josef Janyška (2006)

Archivum Mathematicum

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We describe conditions under which a spacetime connection and a scaled Lorentzian metric define natural symplectic and Poisson structures on the tangent bundle of the Einstein spacetime.

Lectures on generalized complex geometry and supersymmetry

Maxim Zabzine (2006)

Archivum Mathematicum

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These are the lecture notes from the 26th Winter School “Geometry and Physics", Czech Republic, Srní, January 14 – 21, 2006. These lectures are an introduction into the realm of generalized geometry based on the tangent plus the cotangent bundle. In particular we discuss the relation of this geometry to physics, namely to two-dimensional field theories. We explain in detail the relation between generalized complex geometry and supersymmetry. We briefly review the generalized Kähler and...

Lie algebroids and mechanics

Paulette Libermann (1996)

Archivum Mathematicum

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We give a formulation of certain types of mechanical systems using the structure of groupoid of the tangent and cotangent bundles to the configuration manifold $M$ ; the set of units is the zero section identified with the manifold $M$ . We study the Legendre transformation on Lie algebroids.