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