Abstract Narasihman and Ramanan proved in [Amer. J. Math. 83 (1961), 563–572] that an arbitrary connection a vector bundle over base space B can be obtained as the pull-back (via correctly chosen classifying map from into appropriate Grassmannian) of universal Grassmannian. The purpose this paper is to relate geometric properties pulled-back connection. More specifically, we describe conditions...

We introduce a gradient operator that generalizes the Euclidean and Riemannian gradients. This operator acts on sections of vector bundles and is determined by three geometric data: a Riemannian metric on the base manifold, a Riemannian metric and a covariant derivative on the vector bundle. Under the assumption that the covariant derivative is compatible with the metric of the vector bundle, w...

In this paper an almost paracomplex structures on the coframe bundle with Cheeger- Gromoll metric are defined and later we obtained integrability conditions of these structures. Also proved that para-Norden which exists non-Kahler-Norden.

In this paper we study a Riemanian metric on the tangent bundle T (M) of a Riemannian manifold M which generalizes the Cheeger Gromoll metric and a compatible almost complex structure which together with the metric confers to T (M) a structure of locally conformal almost Kählerian manifold. We found conditions under which T (M) is almost Kählerian, locally conformal Kählerian or Kählerian or wh...

The Schrödinger operators on the Newtonian space-time are defined in a way which make them independent on the class of inertial observers. In this picture the Schrödinger operators act not on functions on the space-time but on sections of certain one-dimensional complex vector bundle – the Schrödinger line bundle. This line bundle has trivializations indexed by inertial observers and is associa...