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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Geodesics and conformal transformations of Heisenberg-Reiter spaces


Author: J. F. Torres Lopera
Journal: Trans. Amer. Math. Soc. 306 (1988), 489-498
MSC: Primary 53C22; Secondary 53C25, 53C30
DOI: https://doi.org/10.1090/S0002-9947-1988-0933303-1
MathSciNet review: 933303
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Abstract: Generalized Heisenberg groups, in the sense of Reiter, can be endowed with left-invariant metrics whose geodesies and curvature are obtained. Using these curvature data it is also proved that on their nilmanifolds (compact or not), every conformal transformation is in fact an isometry. A large family of nonisometric examples is given.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0933303-1
Keywords: Generalized Heisenberg group, nilmanifold, geodesic, conformal transformation, Weyl conformal tensor
Article copyright: © Copyright 1988 American Mathematical Society