広島大学総合科学部紀要. IV, 理系編 Volume 28
published_at 2002-12

On 3-Dimensional contact metric manifolds

Kim Byung Hak
Choi Jin Hyuk
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Abstract
Let M be a 3-dimensional almost contact metric manifold satisfying (*)-condition. We denote such amanifold by M*. We prove that if M* is -Einstein, then M* is either Sasakian or cosymplectic manifold, andis a space of constant curvature. Consequently M* is either flat or isometric to the 3-dimensional unit sphereif M* is complete and simply connected.
Keywords
Conformal curvature tensor
almost contact metric manifold
space of constant curvature