Curvature operator of the Bergman metric on a homogeneous bounded domain
نویسندگان
چکیده
منابع مشابه
Infimum of the spectrum of Laplace-Beltrami operator on a bounded pseudoconvex domain with a Kähler metric of Bergman type
where dVg is the volume measure on M with respect to the Kähler metric g. When M is compact and ∆g is uniformly elliptic, λ1(∆g) is the first positive eigenvalue of ∆g with Dirichlet boundary condition. A lot of research has been done on its upper and lower bound estimates and its impact on geometry and physics (see for examples, the lecture notes of P. Li [8] and the paper of S. Udagawa [16] a...
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We obtain a conceptually new differential geometric proof of P.F. Klembeck’s result (cf. [9]) that the holomorphic sectional curvature kg(z) of the Bergman metric of a strictly pseudoconvex domain Ω ⊂ C approaches −4/(n + 1) (the constant sectional curvature of the Bergman metric of the unit ball) as z → ∂Ω.
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It is proved that on any bounded domain in the complex Euclidean space C(n) the Bergman metric is always greater than or equal to the Carathéodory distance. This leads to a number of interesting consequences. Here two such consequences are given. (i) The Bergman metric is complete whenever the Carathéodory distance is complete on a bounded domain. (ii) The Weil-Petersson metric is not uniformly...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1985
ISSN: 0040-8735
DOI: 10.2748/tmj/1178228679