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

Perrone, D. and Vergori, L. (2007) Stability of contact metric manifolds and unit vector fields of minimum energy. Bulletin of the Australian Mathematical Society, 76(2), pp. 269-283. (doi: 10.1017/S0004972700039654)

Abstract

In this paper we obtain criteria of stability for ηEinstein k-contact manifolds, for Sasakian manifolds of constant xs03D5-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 xs03D5-holomorphic sectional curvature +1 minimises the energy functional if and only if M is not simply connected.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Vergori, Dr Luigi
• Authors: Perrone, D., and Vergori, L.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Bulletin of the Australian Mathematical Society
• Publisher: Cambridge University Press
• ISSN: 0004-9727
• ISSN (Online): 1755-1633
• Copyright Holders: Copyright © 2007 Cambridge University Press
• First Published: First published in Bulletin of the Australian Mathematical Society 76(2):269-283
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher