Natural Transformations of Symmetric Affine Connections on Manifolds to Metrics on Linear Frame Bundles: a Classification.
On complete lifts of reductive homogeneous spaces and generalized symmetric spaces
Lifts of generalized symmetric spaces to tangent bundles
On 3-Dimensional Riemannian ...-Spaces.
On the Scalar Curvature of Tangent sphere bundles with Arbitary Constant Radius
Curvatures of the diagonal lift from an affine manifold to the linear frame bundle
We investigate the curvature of the so-called diagonal lift from an affine manifold to the linear frame bundle LM. This is an affine analogue (but not a direct generalization) of the Sasaki-Mok metric on LM investigated by L.A. Cordero and M. de León in 1986. The Sasaki-Mok metric is constructed over a Riemannian manifold as base manifold. We receive analogous and, surprisingly, even stronger results in our affine setting.
Local isometry classes of Riemannian -manifolds with constant Ricci eigenvalues
Three-dimensional conformally flat pseudo-symmetric spaces of constant type
An explicit classification of the spaces in the title is given. The resulting spaces are locally products or locally warped products of the real line and two-dimensional spaces of constant curvature.
Invariance of -natural metrics on linear frame bundles
In this paper we prove that each -natural metric on a linear frame bundle over a Riemannian manifold is invariant with respect to a lifted map of a (local) isometry of the base manifold. Then we define -natural metrics on the orthonormal frame bundle and we prove the same invariance result as above for . Hence we see that, over a space of constant sectional curvature, the bundle with an arbitrary -natural metric is locally homogeneous.
On Riemannian geometry of tangent sphere bundles with arbitrary constant radius
We shall survey our work on Riemannian geometry of tangent sphere bundles with arbitrary constant radius done since the year 2000.
Natural transformations of affine connections on manifolds to metrics on cotangent bundles
On Riemannian manifolds whose tangent sphere bundles can have nonnegative sectional curvature.
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