Kähler metrics generated by functions of the time-like distance in the flat Kähler–Lorentz space |
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Authors: | G. Ganchev V. Mihova |
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Affiliation: | 1. Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, Acad. G. Bonchev Str. bl. 8, 1113 Sofia, Bulgaria;2. Faculty of Mathematics and Informatics, University of Sofia, J. Bouchier Str. 5, (1164) Sofia, Bulgaria |
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Abstract: | We prove that every Kähler metric, whose potential is a function of the time-like distance in the flat Kähler–Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local classification of the Kähler manifolds with the above-mentioned metrics. New examples of Sasakian space forms are obtained as real hypersurfaces of a Kähler space form with special invariant distribution. We introduce three types of even dimensional rotational hypersurfaces in flat spaces and endow them with locally conformal Kähler structures. We prove that these rotational hypersurfaces carry Kähler metrics of quasi-constant holomorphic sectional curvatures satisfying some conditions, corresponding to the type of the hypersurfaces. The meridians of those rotational hypersurfaces, whose Kähler metrics are Bochner–Kähler (especially of constant holomorphic sectional curvatures), are also described. |
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Keywords: | primary 53B35 secondary 53B30 |
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