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HOMOGENEOUS SASAKI AND VAISMAN MANIFOLDS OF UNIMODULAR LIE GROUPS

Part of: Classical differential geometry Automorphic functions Local differential geometry Complex spaces with a group of automorphisms

Published online by Cambridge University Press:  08 November 2019

D. ALEKSEEVSKY Open the ORCID record for D. ALEKSEEVSKY [Opens in a new window] ,
K. HASEGAWA Open the ORCID record for K. HASEGAWA [Opens in a new window]  and
Y. KAMISHIMA Open the ORCID record for Y. KAMISHIMA [Opens in a new window]
D. ALEKSEEVSKY
Affiliation:
Institute for Information Transmission Problems, Bolshoi Karetnyi per., 19, 127994Moscow, Russia email dalekseevsky@iitp.ru
K. HASEGAWA
Affiliation:
Department of Mathematics, Faculty of Education, Niigata University, 8050 Ikarashi-Nino-cho, Nishi-ku, 950-2181Niigata, Japan email hasegawa@ed.niigata-u.ac.jp
Y. KAMISHIMA
Affiliation:
Department of Mathematics, Josai University, Keyaki-dai 1-1, Sakado, 350-0295Saitama, Japan email kami@josai.ac.jp
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Abstract

A Vaisman manifold is a special kind of locally conformally Kähler manifold, which is closely related to a Sasaki manifold. In this paper, we show a basic structure theorem of simply connected homogeneous Sasaki and Vaisman manifolds of unimodular Lie groups, up to holomorphic isometry. For the case of unimodular Lie groups, we obtain a complete classification of simply connected Sasaki and Vaisman unimodular Lie groups, up to modification.

MSC classification

Primary: 32M10: Homogeneous complex manifolds 53A30: Conformal differential geometry
Secondary: 53B35: Hermitian and Kählerian structures

Information

Type
Article
Information
Nagoya Mathematical Journal , Volume 243 , September 2021 , pp. 83 - 96
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Copyright
© 2019 Foundation Nagoya Mathematical Journal

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