Stability of the Reeb vector field of H-contact manifolds

Mathematische Zeitschrift - Tập 263 - Trang 125-147 - 2008
Domenico Perrone1
1Dipartimento di Matematica “Ennio De Giorgi”, Università del Salento, Lecce, Italy

Tóm tắt

It is well known that a Hopf vector field on the unit sphere S 2n+1 is the Reeb vector field of a natural Sasakian structure on S 2n+1. A contact metric manifold whose Reeb vector field ξ is a harmonic vector field is called an H-contact manifold. Sasakian and K-contact manifolds, generalized (k, μ)-spaces and contact metric three-manifolds with ξ strongly normal, are H-contact manifolds. In this paper we study, in dimension three, the stability with respect to the energy of the Reeb vector field ξ for such special classes of H-contact manifolds (and with respect to the volume when ξ is also minimal) in terms of Webster scalar curvature. Finally, we extend for the Reeb vector field of a compact K-contact (2n+1)-manifold the obtained results for the Hopf vector fields to minimize the energy functional with mean curvature correction.

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Mathematische Zeitschrift

Tập 263

125-147

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