This is a survey of recent contributions to the area of special Kaehler
geometry. It is based on lectures given at the 21st Winter School on Geometry
and Physics held in Srni in January 2001

Cortes, Vicente

English

arXiv

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

Cortés, Vincente

Czech digital mathematics library

Special Kaehler manifolds: A survey

Institute of Mathematics AS CR, v. v. i.

http://dml.cz/bitstream/handle/10338.dmlcz/701685/WSGP_21-2001-1_3.pdf

Special Kaehler manifolds: a survey

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Czech digital mathematics library

Institute of Mathematics AS CR, v. v. i.