Abstract
We have studied contact metric hypersurfaces of a Bochner–Kaehler manifold and obtained the following two results: (1) a contact metric constant mean curvature (CMC) hypersurface of a Bochner–Kaehler manifold is a (k, μ)-contact manifold, and (2) if M is a compact contact metric CMC hypersurface of a Bochner–Kaehler manifold with a conformal vector field V that is neither tangential nor normal anywhere, then it is totally umbilical and Sasakian, and under certain conditions on V, is isometric to a unit sphere.
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Ghosh, A., Sharma, R. Contact Hypersurfaces of a Bochner–Kaehler Manifold. Results. Math. 64, 155–163 (2013). https://doi.org/10.1007/s00025-013-0305-y
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DOI: https://doi.org/10.1007/s00025-013-0305-y