Abstract
We prove that a bicontact metric three-manifold either is flat or admits some positive sectional curvature at any point. In particular, the Blair's conjecture is true for a bicontact metric three-manifold. Moreover, we prove that a contact metric three-manifold for which the contact distribution cannot be decomposed as a sum of two one-dimensional distributions, admits some positive sectional curvature; this extends the main result of [4].
Citation
Domenico Perrone. "On the Blair's conjecture for contact metric three-manifolds." Tohoku Math. J. (2) 75 (4) 527 - 532, 2023. https://doi.org/10.2748/tmj.20220530
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