Vaisman structures on compact solvmanifolds

Let ( M , g , J ) be a compact Hermitian manifold and Ω the fundamental 2-form of ( g , J ) . A Hermitian manifold ( M , g , J ) is said to be locally conformal Kähler if there exists a closed 1-form ω such that d Ω = ω ∧ Ω . In this paper, we prove that a Vaisman structure on compact locally confor...

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Bibliographic Details
Published in:Geometriae dedicata 2015-10, Vol.178 (1), p.389-404
Main Author: Sawai, Hiroshi
Format: Article
Language:English
Subjects:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
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Summary:Let ( M , g , J ) be a compact Hermitian manifold and Ω the fundamental 2-form of ( g , J ) . A Hermitian manifold ( M , g , J ) is said to be locally conformal Kähler if there exists a closed 1-form ω such that d Ω = ω ∧ Ω . In this paper, we prove that a Vaisman structure on compact locally conformal Kähler solvmanifolds is depend on only the form of the fundamental 2-form Ω .
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-015-0062-z