Geodesic
$g$-natural metrics of constant curvature on unit tangent sphere bundles
Archivum mathematicum, Tome 48 (2012) no. 2, pp. 81-95.

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We completely classify Riemannian $g$-natural metrics of constant sectional curvature on the unit tangent sphere bundle $T_1 M$ of a Riemannian manifold $(M,g)$. Since the base manifold $M$ turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian $g$-natural metric on the unit tangent sphere bundle of a Riemannian surface.
DOI : 10.5817/AM2012-2-81
Classification : 53C15, 53C25, 53D10
Keywords: unit tangent sphere bundle; $g$-natural metric; curvature tensor; contact metric geometry 
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     title = {$g$-natural metrics of constant curvature on unit tangent sphere bundles},
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     pages = {81--95},
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Abbassi, M. T. K.; Calvaruso, G. $g$-natural metrics of constant curvature on unit tangent sphere bundles. Archivum mathematicum, Tome 48 (2012) no. 2, pp. 81-95. doi : 10.5817/AM2012-2-81. http://geodesic.mathdoc.fr/articles/10.5817/AM2012-2-81/

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