Abstract.
We study the geometric properties of the base manifold for the unit tangent bundle satisfying the η-Einstein condition with the canonical contact metric structure. One of the main theorems is that the unit tangent bundle of 4-dimensional Einstein manifold, equipped with the canonical contact metric structure, is η-Einstein manifold if and only if the base manifold is the space of constant sectional curvature 1 or 2.
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Authors’ addresses: Y. D. Chai, S. H. Chun, J. H. Park, Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea; K. Sekigawa, Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-2181, Japan
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Chai, Y., Chun, S., Park, J. et al. Remarks on η-Einstein unit tangent bundles. Monatsh Math 155, 31–42 (2008). https://doi.org/10.1007/s00605-008-0534-4
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DOI: https://doi.org/10.1007/s00605-008-0534-4