We introduce a new family of Riemannian metrics on the three-sphere and study its geometric properties, starting from the description of their curvature. Such metrics, which include the standard metric and Berger metrics as special cases, are called “of Kaluza–Klein type”, because they are induced in a natural way by the corresponding metrics defined on the tangent sphere bundle of the two-sphere.
Geometry of Kaluza–Klein metrics on the sphere $S^3$
CALVARUSO, Giovanni;PERRONE, Domenico
2012-01-01
Abstract
We introduce a new family of Riemannian metrics on the three-sphere and study its geometric properties, starting from the description of their curvature. Such metrics, which include the standard metric and Berger metrics as special cases, are called “of Kaluza–Klein type”, because they are induced in a natural way by the corresponding metrics defined on the tangent sphere bundle of the two-sphere.File in questo prodotto:
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