A new look at adapted complex structures
On a closed real analytic Riemannian manifold a one-parameter family of adapted complex structures on the total space of the tangent bundle is constructed. For parameters \(s\in \mathbb C\setminus\mathbb R\), this is a Kähler structure, which for the particular value \(s=i\) was investigated before by \textit{V. Guillemin} and \textit{M. Stenzel} [J. Differ. Geom. 34, No. 2, 561--570 (1991; Zbl 0746.32005)] and \textit{L. Lempert} and \textit{R. Szőke} [Math. Ann. 290, No. 4, 689--712 (1991; Zbl 0752.32008)]. For real parameters \(s\), the structure is real polarized. The results are announced to be applicable to geometric quantization.
scientific article; zbMATH DE number 6023881