$g$-natural metrics of constant curvature on unit tangent sphere bundles

M. T. K. Abbassi and G. Calvaruso

Address:
Département des Mathématiques, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdallah, B.P. 1796, Fès-Atlas, Fès, Morocco
Dipartimento di Matematica “E. De Giorgi”, Università degli Studi di Lecce, Lecce, Italy

E-mail:
mtk_abbassi@Yahoo.fr
giovanni.calvaruso@unile.it

Abstract: 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.

AMSclassification: primary 53D10; secondary 53C15, 53C25.

Keywords: unit tangent sphere bundle, g-natural metric, curvature tensor, contact metric geometry.

DOI: 10.5817/AM2012-2-81