# Article

 Title: Special Kaehler manifolds: A survey (English) Author: Cortés, Vincente Language: English Journal: Proceedings of the 21st Winter School "Geometry and Physics" Volume: Issue: 2001 Year: Pages: [11]-18 . Category: math . Summary: This is a survey of recent contributions to the area of special K\"ahler geometry. A (pseudo-)K\"ahler 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 K\"ahler manifold $(M,J,g,\nabla)$ is a K\"ahler manifold $(M,J,g)$ together with a flat torsionfree connection $\nabla$ such that i) $\nabla \omega = 0,$ where $\omega = g(.,J.)$ is the K\"ahler form and ii) $\nabla$ is symmetric. A holomorphic immersion $\phi : M \rightarrow V$ is called K\"ahlerian if $\phi^{\star} \gamma$ is nondegenerate and it is called Lagrangian if $\phi^{\star}\Omega= 0.$\par Theorem 1. Let $\phi:M \rightarrow V$ be a K\"ahlerian Lagrangian immersion with induced geometric data $(g,\nabla).$ Then $(M,J,g,\nabla)$ is a special K\"ahler manifold. Conversely, any simply connected sp! (English) MSC: 32Q15 MSC: 32Q20 MSC: 53C26 MSC: 53C55 idZBL: Zbl 1039.53079 idMR: MR1972422 . Date available: 2009-07-13T21:46:31Z Last updated: 2012-09-18 Stable URL: http://hdl.handle.net/10338.dmlcz/701685 .

## Files

Files Size Format View
WSGP_21-2001-1_3.pdf 759.5Kb application/pdf View/Open

Partner of