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Let ${\bar{L}}_{i} \to X_{i}$ be a holomorphic line bundle over a compact complex manifold for $i = 1, 2$ . Let $S_{i}$ denote the associated principal circle-bundle with respect to some hermitian inner product on ${\bar{L}}_{i}$ . We construct complex structures on $S = S_{1} \times S_{2}$ which we refer to as scalar, diagonal, and linear types. While scalar type structures always exist, the more general diagonal but non-scalar type structures are constructed assuming that ${\bar{L}}_{i}$ are equivariant ${(ℂ^{*})}^{n_{i}}$ -bundles satisfying some additional conditions. The linear type complex structures...

Complexifications of Transversely Holomorphic.

A. Haefliger, D. Sundararaman (1985)

Mathematische Annalen

Convergence of Bergman geodesics on ${CP}^{1}$

Jian Song, Steve Zelditch (2007)

Annales de l’institut Fourier

The space $ℋ$ of Kähler metrics in a fixed Kähler class on a projective Kähler manifold $X$ is an infinite dimensional symmetric space whose geodesics $ω_{t}$ are solutions of a homogeneous complex Monge-Ampère equation in $A \times X$ , where $A \subset ℂ$ is an annulus. Phong-Sturm have proven that the Monge-Ampère geodesic of Kähler potentials $ϕ (t, z)$ of $ω_{t}$ may be approximated in a weak $C^{0}$ sense by geodesics $ϕ_{N} (t, z)$ of the finite dimensional symmetric space of Bergman metrics of height $N$ . In this article we prove that $ϕ_{N} (t, z) \to ϕ (t, z)$ in $C^{2} ([0, 1] \times X)$ in the case of...

Curvature properties of the Calabi-Yau moduli.

Wang, Chin-Lung (2003)

Documenta Mathematica

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