Unit Tangent Sphere Bundles with Constant Scalar Curvature

Classification of 4-dimensional homogeneous weakly einstein manifolds

“…Let g 3 be a unimodular Lie algebra with a scalar product , 3 . According to [10], page 305, there is an orthonormal basis {f 1 , f 2 , f 3 } of g 3 such that (2.1) […”

“…Let r 3 be the Lie algebra of R 3 with a scalar product , 3 . The algebra of all derivations D of r 3 is gl(3, R).…”

“…It is known from [3] that, for n = 4, the constancy of |R| is automatically satisfied. Thus, the dimension 4 is the most interesting case.…”

The Holomorphic φ-Sectional Curvature of Tangent Sphere Bundles with Sasakian Structures

“…The geometry of the tangent sphere bundles of constant radius r, endowed with the metrics induced by some Riemannian metrics from the ambient tangent bundle, was studied by authors like Abbassi, Boeckx, Calvaruso, Kowalski, Munteanu, Park, Sekigawa, Sekizawa (see [1], [2], [4]- [7], [9], [12]- [14], [16]). In the most part of the papers, such as [4], [5] and [16], the metric considered on the tangent bundle T M was the Sasaki metric, but Boeckx noticed that the unit tangent bundle equipped with the induced Cheeger-Gromoll metric is isometric to the tangent sphere bundle T 1…”

“…In the most part of the papers, such as [4], [5] and [16], the metric considered on the tangent bundle T M was the Sasaki metric, but Boeckx noticed that the unit tangent bundle equipped with the induced Cheeger-Gromoll metric is isometric to the tangent sphere bundle T 1…”