Affine hyperspheres associated to special para-Kähler manifolds

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Erscheinungsjahr:
2006
Medientyp:
Text
Schlagworte:
  • Affine hyperspheres
  • Constant mean curvature
  • Special para-Kähler manifolds
Beschreibung:
  • We prove that any special para-Kähler manifold is intrinsically an improper affine hypersphere. As a corollary, any para-holomorphic function F of n para-complex variables satisfying a non-degeneracy condition defines an improper affine hypersphere, which is the graph of a real function f of 2n variables. We give an explicit formula for the function f in terms of the para-holomorphic function F. Necessary and sufficient conditions for an affine hypersphere to admit the structure of a special para-Kähler manifold are given. Finally, it is shown that conical special para-Kähler manifolds are foliated by proper affine hyperspheres of constant mean curvature. © 2006 World Scientific Publishing Company.
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  • info:eu-repo/semantics/closedAccess
Quellsystem:
Forschungsinformationssystem der UHH
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oai:www.edit.fis.uni-hamburg.de:publications/9e7fdffb-a3fb-403b-ae47-df1ec39c608d