Special Kaehler manifolds: A survey

Cortés, Vincente

Proceedings of the 21st Winter School "Geometry and Physics", GDML_Books, (2002), p. [11]-18 / Harvested from

Résumé

This is a survey of recent contributions to the area of special Kähler geometry. A (pseudo-)Kähler manifold $(M,J,g)$ is a differentiable manifold endowed with a complex structure $J$ and a (pseudo-)Riemannian metric $g$ such that i) $J$ is orthogonal with respect to the metric $g,$ ii) $J$ is parallel with respect to the Levi Civita connection $D.$ A special Kähler manifold $(M,J,g,\nabla )$ is a Kähler manifold $(M,J,g)$ together with a flat torsionfree connection $\nabla $ such that i) $\nabla \omega = 0,$ where $\omega = g(.,J.)$ is the Kähler form and ii) $\nabla $ is symmetric. A holomorphic immersion $\phi : M \rightarrow V$ is called Kählerian if $\phi ^{\star } \gamma $ is nondegenerate and it is called Lagrangian if $\phi ^{\star }\Omega = 0.$Theorem 1. Let $\phi :M \rightarrow V$ be a Kählerian Lagrangian immersion with induced geometric data $(g,\nabla ).$ Then $(M,J,g,\nabla )$ is a special Kähler manifold. Conversely, any simply connected sp!

Détail

MR MR1972422 | Zbl 1039.53079

EUDML-ID : urn:eudml:doc:221089
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