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 $\phi :M\to V$ is called Kählerian if ${\phi }^{☆}\gamma$ is nondegenerate and it is called Lagrangian if ${\phi }^{☆}\Omega =0.$Theorem 1. Let $\phi :M\to V$ 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!

EUDML-ID : urn:eudml:doc:221089
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@article{701685,
     title = {Special Kaehler manifolds: A survey},
     booktitle = {Proceedings of the 21st Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2002},
     pages = {[11]-18},
     mrnumber = {MR1972422},
     zbl = {1039.53079},
     url = {http://dml.mathdoc.fr/item/701685}
}

Cortés, Vincente. Special Kaehler manifolds: A survey, dans Proceedings of the 21st Winter School "Geometry and Physics", GDML_Books,  (2002), pp. [11]-18. http://gdmltest.u-ga.fr/item/701685/