We show that the unit tangent bundle of S4 and a real cohomology CP 3 admit Riemannian metrics with positive sectional curvature almost everywhere. These are the only examples so far with positive curvature almost everywhere that are not also known to admit positive curvature. AMS Classi cation numbers Primary: 53C20 Secondary: 53C20, 58B20, 58G30

the geometry of a system of second order differential equations is the geometry of a semispray, which is a globally defined vector field on tm. the metrizability of a given semispray is of special importance. in this paper, the metric associated with the semispray s is applied in order to study some types of foliations on the tangent bundle which are compatible with sode structure. indeed, suff...

fibre is the re-dimensional complex projective space (complex projective co-tangent bundle). This bundle of complex dimension 2re + l is our M. Considering the fibre of T(V) as the (2w+2)-dimensional real vector space, we take as P the co-tangent sphere bundle over V (i.e., the fibre of P is a sphere in the fibre of T(V)). T(V) — V is the principal fibre bundle associated with a line bundle L o...

A tangent manifold is a pair (M, J) with J a tangent structure (J2 = 0, ker J = im J) on the manifold M . A systematic study of tangent manifolds was done by I. Vaisman in [5]. One denotes by HM any complement of im J := TV . Using the projections h and v on the two terms in the decomposition TM = HM ⊕TV one naturally defines an almost complex structure F on M . Adding to the pair (M, J) a Riem...

Let $(M^{m}, g)$ be a Riemannian manifold and $TM$ its tangent bundle equipped with deformed Sasaki metric. In this paper, firstly we investigate all forms of curvature tensors (Riemannian tensor, Ricci curvature, sectional scalar curvature). Secondly, study the geometry unit metric, where presented formulas Levi-Civita connection also

Unit tangent bundle of a surface carries various information of tangent vector fields on that surface. For 2-spheres (i.e. genus-zero closed surfaces), the unit tangent bundle is a closed 3-manifold that has non-trivial topology and cannot be embedded in R. Therefore it cannot be constructed by existing mesh generation algorithms directly. This work aims at the first discrete construction of un...

The geometry of a system of second order differential equations is the geometry of a semispray, which is a globally defined vector field on TM. The metrizability of a given semispray is of special importance. In this paper, the metric associated with the semispray S is applied in order to study some types of foliations on the tangent bundle which are compatible with SODE structure. Indeed, suff...

1. a) Compute the Stiefel-Whitney classes of the tangent bundle of RP . (Use the method from class for the tangent Chern classes of complex projectives spaces.) b) Conclude that if the tangent bundle is trivial, then n = 2 − 1 for some m. (In fact n must be 0, 1, 3, 7, but this is much harder to prove; one proof uses the Bott periodicity theorem.) c) Deduce (very easily!) a complete characteriz...