Abstract
In the present chapter we deal with harmonic forms and holomorphic forms and vector fields on compact Vaisman manifolds using the method in [275]. One of the main results is a partial answer to Vaisman’s conjectures:A compact g.H. manifold has an odd first Betti number.We shall also study the relation between holomorphic and Killing vector fields and give a certain answer to the question: How many l.c.K. metrics exist on a compact g.H. manifold?
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© 1998 Springer Science+Business Media New York
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Dragomir, S., Ornea, L. (1998). Harmonic and holomorphic forms. In: Locally Conformal Kähler Geometry. Progress in Mathematics, vol 155. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2026-8_7
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DOI: https://doi.org/10.1007/978-1-4612-2026-8_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7387-5
Online ISBN: 978-1-4612-2026-8
eBook Packages: Springer Book Archive