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Stability of contact metric manifolds and unit vector fields of minimum energy

Published online by Cambridge University Press:  17 April 2009

D. Perrone  and
L. Vergori
D. Perrone
Affiliation:
Dipartimento di Matematica “Ennio De Giorgi”, Università di Lecce, 73100, Lecce, Italy, e-mail: domenico.perrone@unile.it, luigi.vergori@unile.it
L. Vergori
Affiliation:
Dipartimento di Matematica “Ennio De Giorgi”, Università di Lecce, 73100, Lecce, Italy, e-mail: domenico.perrone@unile.it, luigi.vergori@unile.it
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In this paper we obtain criteria of stability for ηEinstein k-contact manifolds, for Sasakian manifolds of constant ϕ-sectional curvature and for 3-dimensional Sasakian manifolds. Moreover, we show that a stable compact Einstein contact metric manifold M is Sasakian if and only if the Reeb vector field ξ minimises the energy functional. In particular, the Reeb vector field of a Sasakian manifold M of constant ϕ-holomorphic sectional curvature +1 minimises the energy functional if and only if M is not simply connected.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 76 , Issue 2 , October 2007 , pp. 269 - 283
Copyright
Copyright © Australian Mathematical Society 2007

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