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

M. T. K. Abbassi, Giovanni Calvaruso (2012)

Archivum Mathematicum

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.

Generalized m-quasi-Einstein metric within the framework of Sasakian and K-contact manifolds

Amalendu Ghosh (2015)

Annales Polonici Mathematici

We consider generalized m-quasi-Einstein metric within the framework of Sasakian and K-contact manifolds. First, we prove that a complete Sasakian manifold M admitting a generalized m-quasi-Einstein metric is compact and isometric to the unit sphere S 2 n + 1 . Next, we generalize this to complete K-contact manifolds with m ≠ 1.

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