Geodesic
Lectures on generalized complex geometry and supersymmetry
Archivum mathematicum, Tome 42 (2006) no. 5, pp. 119-146.

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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 generalized Calabi-Yau manifolds and explain their appearance in physics.
Classification : 53C15, 53D17 
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Zabzine, Maxim. Lectures on generalized complex geometry and supersymmetry. Archivum mathematicum, Tome 42 (2006) no. 5, pp. 119-146. http://geodesic.mathdoc.fr/item/ARM_2006__42_5_a3/