A Classification of Compact Cohomogeneity One Locally Conformal Kähler Manifolds

Autor:	Daniel Guan
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	cohomology invariant structure homogeneous space cohomogeneity one complex torus bundles Hermitian manifolds Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 11, p 1710 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12111710
Popis:	In this paper, we apply a result of the classification of a compact cohomogeneity one Riemannian manifold with a compact Lie group G to obtain a classification of compact cohomogeneity one locally conformal Kähler manifolds. In particular, we prove that the compact complex manifold is a complex one-dimensional torus bundle over a projective rational homogeneous, or cohomogeneity one manifold except of a class of manifolds with a generalized Hopf surface bundle over a projective rational homogeneous space. Additionally, it is a homogeneous compact complex manifold under the complexification GC of the given compact Lie group G under an extra condition that the related closed one form is cohomologous to zero on the generic G orbit. Moreover, the semi-simple part S of the Lie group action has hypersurface orbits, i.e., it is of cohomogeneity one with respect to the semi-simple Lie group S in that special case.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/da8cb71e7c994488af0ccf6ff5083b37 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
Nepřihlášeným uživatelům se plný text nezobrazuje	K zobrazení výsledku je třeba se přihlásit.