1,720,974 research outputs found
Berezin quantization of homogeneous bounded domains
No full textWe prove that a homogeneous bounded domain admits a Berezin quantizatio
Uniqueness of balanced metrics on complex vector bundles.
No full textLet E → M be a holomorphic vector bundle over a compact Kähler manifold (M,ω). We prove that if E admits a ω-balanced metric (in X. Wang’s terminology (Wang, 2005 [3])) then it is unique. This result together with Biliotti and Ghigi (2008) [14] implies the existence and uniqueness of ω-balanced metrics of certain direct sums of irreducible homogeneous vector bundles over rational homogeneous varieties. We finally apply our result to show the rigidity of ω-balanced Kähler maps into Grassmannians
Rigidity properties of holomorphic isometries into homogeneous K\"{a}hler manifolds
Full text linkWe prove two rigidity results on holomorphic isometries into homogeneous
K\"{a}hler manifolds. The first shows that a K\"{a}hler-Ricci soliton induced
by the homogeneous metric of the K\"{a}hler product of a special flag manifold
(i.e. a flag of classical type or integral type) with a bounded homogeneous
domain is trivial, i.e. K\"{a}hler-Einstein. In the second one we prove that:
(i) a flat space is not relative to the K\"{a}hler product of a special flag
manifold with a homogeneous bounded domain, (ii) a special flag manifold is not
relative to the K\"{a}hler product of a flat space with a homogeneous bounded
domain and (iii) a homogeneous bounded domain is not relative to the K\"{a}hler
product of a flat space with a special flag manifold. Our theorems strongly
extend the results in [4], [5], [12], [13] and [22].Comment: 14 page
A Cartan–Hartogs version of the polydisk theorem
Full text linkWe extend the Polydisk Theorem for symmetric bounded domains to Cartan–Hartogs domains, and apply it to prove that a Cartan–Hartogs domain inherits totally geodesic submanifolds from the bounded symmetric domain which is based on, and to give a characterization of Cartan–Hartogs’s geodesics with linear support
Symplectic geometry of Cartan–Hartogs domains
Full text linkThis paper studies the geometry of Cartan–Hartogs domains from the symplectic point of view. Inspired by duality between compact and noncompact Hermitian symmetric spaces, we construct a dual counterpart of Cartan–Hartogs domains and give explicit expression of global Darboux coordinates for both Cartan–Hartogs domains and their dual. Further, we compute their symplectic capacity and show that a Cartan–Hartogs domain admits a symplectic duality if and only if it reduces to be a complex hyperbolic space
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