Article history: Received 10 July 2013 Available online 17 April 2014 Communicated by D.V. Alekseevsky MSC: primary 53C21 secondary 53C20 We classify the triples H ⊂ K ⊂ G of nested compact Lie groups which satisfy the “positive triple” condition that was shown in [17] to ensure that G/H admits a metric with quasi-positive curvature. A few new examples of spaces that admit quasi-positively curv...

Based on the usual Fedosov construction of star products for a symplectic manifold M we give a simple geometric construction of a bimodule deformation for the sections of a vector bundle over M starting with a symplectic connection on M and a connection for E. In the case of a line bundle this gives a Morita equivalence bimodule where the relation between the characteristic classes of the Morit...

For a homogeneous space G/P , where P is a parabolic subgroup of a complex semisimple group G, an explicit Kähler–Einstein metric on it is constructed. The Einstein constant for the metric is 1. Therefore, the intersection number of the first Chern class of the holomorphic tangent bundle of G/P coincides with the volume of G/P with respect to this Kähler–Einstein metric, thus enabling us to com...

For any ε > 0, we construct an explicit smooth Riemannian metric on the sphere Sn, n ≥ 3, that is within ε of the round metric and has a geodesic for which the corresponding orbit of the geodesic flow is ε-dense in the unit tangent bundle. Moreover, for any ε > 0, we construct a smooth Riemannian metric on S, n ≥ 3, that is within ε of the round metric and has a geodesic for which the complemen...

Consider a real n-plane bundle ξ with Euclidean metric. Associated to ξ are a number of auxiliary bundles: disc bundle, sphere bundle, projective bundle, k-frame bundle, etc. Here “bundle” simply means a local product with the indicated fibre. In each case one can show, by easy but repetitive arguments, that the projection map in question is indeed a local product; furthermore, the transition f...

The concepts of relative velocity and acceleration, deviation velocity and acceleration and relative momentum of point particles in spaces (manifolds), the tangent bundle of which is equipped with a transport along paths, are introduced. If the tangent bundle is endowed also with a metric, it gives rise also to the notion of a relative energy. Certain ties between these quantities are considere...

A complete noncompact manifold M with nonnegative sectional curvature is diffeomorphic to the normal bundle of a compact submanifold S called the soul of M . When S is a round sphere we show that the clutching map of this bundle is restricted; this is used to deduce that there are at most finitely many isomorphism types of such bundles with sectional curvature lying in a fixed interval [0, κ]. ...

We give a method to construct Calabi-Yau metrics on G-invariant vector bundles over Kähler coset spaces G/H using supersymmetric nonlinear realizations with matter coupling. As a concrete example we discuss the CPN model coupled with matter. The canonical line bundle is reproduced by the singlet matter and the cotangent bundle with a new non-compact Calabi-Yau metric which is not hyper-Kähler i...

In this paper we study a Riemanian metric on the tangent bundle T (M) of a Riemannian manifoldM which generalizes Sasakian metric and Cheeger–Gromoll metric along a compatible almost complex structure which together with the metric confers to T (M) a structure of locally conformal almost Kählerian manifold. This is the natural generalization of the well known almost Kählerian structure on T (M)...

The canonical family of Thom forms s for 0 < s < 1 constructed by Harvey and Lawson on an oriented real vector bundle V ! X with metric connection D V is shown to have a smooth current extension to the bundle of real projective spaces, P(R V) ! X, which compactiies V in the bre directions. The current limit as r ! 1 and s ! 0 of the smooth transgression formula r ? s = r;s is the current equation