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- W2941874461 abstract "In this paper, we provide a complete description of Vaisman structures on certain principal elliptic bundles over complex flag manifolds, this description allows us to classify homogeneous l.c.K. structures on compact homogeneous Hermitian manifolds. Moreover, as an application of the latter result, through these structures we explicitly describe all homogeneous Hermitian metrics which solve the Hermitian-Einstein-Weyl equation on compact homogeneous Hermitian-Weyl manifolds. The main feature of our approach is to employ elements of representation theory of simple Lie algebras to describe Cartan-Ehresmann connections on principal elliptic bundles over complex flag manifolds. Further, we also present a characterization for Kahler covering of compact homogeneous l.c.K. manifolds as regular locus of certain Stein spaces (with isolated singularity) defined by the complex analytification of HV-varieties, a.k.a. Kostant cones. This characterization of Kahler covering allows us to describe the Kodaira-type embedding for compact homogeneous l.c.K. manifolds purely in terms of elements of representation theory of semisimple complex algebraic groups." @default.
- W2941874461 created "2019-05-03" @default.
- W2941874461 creator A5013244944 @default.
- W2941874461 date "2019-04-23" @default.
- W2941874461 modified "2023-09-27" @default.
- W2941874461 title "Principal elliptic bundles and compact homogeneous l.c.K. manifolds" @default.
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