On Tangent Sphere Bundles with Small or Large Constant Radius

For a Riemannian manifold M, we determine somecurvature properties of a tangent sphere bundleT _r M endowed with the induced Sasaki metric in the case when the constantradius r > 0 of the tangent spheres is either sufficientlysmall or sufficiently large.     

On the Geometry of the （1, 1）-Tensor Bundle with Sasaki Type Metric

Curvature properties are studied for the Sasaki metric on the (1,1) tensor bundle of a Riemannian manifold. As an application, examples of almost para-Nordenian and para-K(a)hler-Nordenian B-metrics are constructed on the (1,1) tensor bundle by looking at the Sasaki metric. Also, with respect to the para-Nordenian B-structure, paraholomorphic conditions for the complete lifts of vector fields are analyzed.