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- Title
A Classification of Compact Cohomogeneity One Locally Conformal Kähler Manifolds.
- Authors
Guan, Daniel
- Abstract
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 G C 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.
- Subjects
SEMISIMPLE Lie groups; COMPACT groups; HOMOGENEOUS spaces; COMPLEX manifolds; LIE groups; ORBITS (Astronomy); RIEMANNIAN manifolds
- Publication
Mathematics (2227-7390), 2024, Vol 12, Issue 11, p1710
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math12111710