Special Kaehler manifolds: A survey

Cortés, Vincente. "Special Kaehler manifolds: A survey." Proceedings of the 21st Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2002. [11]-18. <http://eudml.org/doc/221089>.

@inProceedings{Cortés2002,
abstract = {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!},
author = {Cortés, Vincente},
booktitle = {Proceedings of the 21st Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {[11]-18},
publisher = {Circolo Matematico di Palermo},
title = {Special Kaehler manifolds: A survey},
url = {http://eudml.org/doc/221089},
year = {2002},
}

TY - CLSWK
AU - Cortés, Vincente
TI - Special Kaehler manifolds: A survey
T2 - Proceedings of the 21st Winter School "Geometry and Physics"
PY - 2002
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [11]
EP - 18
AB - 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!
KW - Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/221089
ER -