Tohoku Mathematical Journal
2023
December
SECOND SERIES VOL. 75, NO. 4

Tohoku Math. J.
75 (2023), 527-532

Title ON THE BLAIR'S CONJECTURE FOR CONTACT METRIC THREE-MANIFOLDS

Dedicated to the memory of Professor L. Vanhecke
Author Domenico Perrone

(Received December 21, 2021, revised May 11, 2022)
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].

Mathematics Subject Classification. Primary 53C15; Secondary 53D10, 53C25.
Key words and phrases. Blair's conjecture, contact and bi-contact metric structures, three-manifolds.

To the top of this page

Back to the Contents