Showing papers on "Unit tangent bundle published in 1975"

Smoothness of horocycle foliations

Abstract: Author(s): Hirsch, MW; Pugh, CC | Abstract: The geodesic flow on the unit tangent bundle of a Riemannian manifold M is smooth.if the curvature of M is 1/4-pinched..

Selfadjoint metrics on almost tangent manifolds whose Riemannian connection is almost tangent

Abstract: Let M be a differentiable manifold of class C ∞, with a given (1, 1) tensor field J of constant rank such that J2=λI (for some real constant λ). J defines a class of conjugate (G-structures on M. For λ>0, one particular representative structure is an almost product structure. Almost complex structure arises when λ<0. If the rank of J is maximum and λ=0, then we obtain an almost tangent structure. In the last two cases the dimension of the manifold is necessarily even. A Riemannian metric S on M is said to be related if one of the conjugate structures defined by S has a common subordinate structure with the G-structure defined by S. It is said to be J-metric if the orthogonal structure defined by S has a common subordinate structure.

The structural consideration of the tangent bundleT(M n ) withg M over a riemannian manifoldM n

Abstract: A refinement of the geometry of tangent bundle[9] is made by presenting the proposition((2.3)) on tensor fields of a tangent bundle and it is shown that the Riemann metric gM of a tangent bundle previously called the Sasaki lift is nothing but the direct sum of the vertical and horizontal lift of the Riemann metric defined on the base Riemann manifold. The geometric meaning of the unit tensor field and the almost complex structure is given on the basis of the proposition((2.3)). By means of B. O’Neill’s scheme and of Y. Muto’s notion the geometry of horizontal and vertical distribution is developed and it is shown that the fibre is totally geodesic while the horizontal distribution admits the second fundamental tensor field which is skew-symmetric. In Y. Muto’s sense the tangent bundle with gM is an isometric and parallel fibred space.

On an invariant of a bundle of quadrics

Abstract: It is shown how the Hesse curve and theta-characteristic of a bundle of quadrics can be used to reconstruct the initial bundle. The corresponding construction is used to prove the global Torelli theorem for the intersection of three quadrics.Bibliography: 2 items