Almost contact metric manifolds whose Reeb vector field is a harmonic section

作者：Perrone D^*

来源：Acta Mathematica Hungarica, 2013, 138(1-2): 102-126.

DOI：10.1007/s10474-012-0228-1

• harmonic unit vector field
• harmonic almost contact metric structure
• locally conformal cosymplectic manifold
• almost Kenmotsu manifold
• almost contact metric three-manifold
• almost cosymplectic manifold
• (kappa, mu)-space

We investigate almost contact metric manifolds whose Reeb vector field is a harmonic unit vector field, equivalently a harmonic section. We first consider an arbitrary Riemannian manifold and characterize the harmonicity of a unit vector field xi, when a double dagger xi is symmetric, in terms of Ricci curvature. Then, we show that for the class of locally conformal almost cosymplectic manifolds whose Reeb vector field xi is geodesic, xi is a harmonic section if and only if it is an eigenvector of the Ricci operator. Moreover, we build a large class of locally conformal almost cosymplectic manifolds whose Reeb vector field is a harmonic section. Finally, we exhibit several classes of almost contact metric manifolds where the associated almost contact metric structures sigma are harmonic sections, in the sense of Vergara-Diaz and Wood [25], and in some cases they are also harmonic maps.

• 出版日期2013-1