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φ-symmetriccontact metric spaces

Published online by Cambridge University Press:  01 October 1999

E. Boeckx ,
P. Bueken  and
L. Vanhecke
E. Boeckx
Affiliation:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium. E-mail:eric.boeckx@wis.kuleuven.ac.be; peter.bueken@wis.kuleuven.ac.be; lieven.vanhecke@wis.kuleuven.ac.be
P. Bueken
Affiliation:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium. E-mail:eric.boeckx@wis.kuleuven.ac.be; peter.bueken@wis.kuleuven.ac.be; lieven.vanhecke@wis.kuleuven.ac.be
L. Vanhecke
Affiliation:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium. E-mail:eric.boeckx@wis.kuleuven.ac.be; peter.bueken@wis.kuleuven.ac.be; lieven.vanhecke@wis.kuleuven.ac.be
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Abstract

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We give the first examples of contact metric spaces which are weakly locally $\varphi$-symmetric (that is, $\nabla R=0$ on horizontal vectors), but not strongly (that is, not all reflections with respect to the characteristic lines are local isometries). These examples are three-dimensional non-unimodular Lie groups with a left-invariant contact metric structure. We exhibit additional symmetries on these spaces.

1991 Mathematics Subject Classification: 53B20, 53C15, 53C25.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 41 , Issue 3 , October 1999 , pp. 409 - 416
Copyright
1999 Glasgow Mathematical Journal Trust