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- Title
Contact metric manifolds with large automorphism group and (κ, μ)-spaces.
- Authors
Lotta, Antonio
- Abstract
We discuss the classification of simply connected, complete (κ, μ)-spaces from the point of view of homogeneous spaces. In particular, we exhibit new models of (κ, μ)-spaces having Boeckx invariant -1. Finally, we prove that the number (n+1)(n+2)/2 is the maximum dimension of the automorphism group of a contact metric manifold of dimension 2n + 1, n ≥ 2, whose symmetric operator h has rank at least 3 at some point; if this dimension is attained, and the dimension of the manifold is not 7, it must be a (κ, μ)-space. The same conclusion holds also in dimension 7 provided the almost CR structure of the contact metric manifold under consideration is integrable.
- Subjects
AUTOMORPHISMS; CONTACT manifolds; HOMOGENEOUS spaces; SYMMETRIC spaces; MANIFOLDS (Mathematics); SYMMETRIC operators
- Publication
Complex Manifolds, 2019, Vol 6, Issue 1, p294
- ISSN
2300-7443
- Publication type
Article
- DOI
10.1515/coma-2019-0015