Smoothing locally flat imbeddings of differentiable manifolds

Imbeddings, Immersions, and Cobordism of Differentiable Manifolds

Differentiable Imbeddings

1. Terminology. V and M will be differentiable manifolds of dimension n and m respectively; differentiable meaning always of class C. For simplicity, we assume V compact and without boundary. We shall have to consider several categories of maps: (1) the category of continuous maps, (2) the category of topological imbeddings, (3) the category of topological immersions: a map ƒ: F—>M is a topolog...

Geometric Inequalities on Locally Conformally Flat Manifolds

In this paper, we are interested in certain global geometric quantities associated to the Schouten tensor and their relationship in conformal geometry. For an oriented compact Riemannian manifold (M,g) of dimension n > 2, there is a sequence of geometric functionals arising naturally in conformal geometry, which were introduced by Viaclovsky in [29] as curvature integrals of Schouten tensor. If...

Locally conformal flat Riemannian manifolds with constant principal Ricci curvatures and locally conformal flat C-spaces

It is proved that every locally conformal flat Riemannian manifold all of whose Jacobi operators have constant eigenvalues along every geodesic is with constant principal Ricci curvatures. A local classification (up to an isometry) of locally conformal flat Riemannian manifold with constant Ricci eigenvalues is given in dimensions 4, 5, 6, 7 and 8. It is shown that any n-dimensional (4 ≤ n ≤ 8)...

BOUNDARIES OF LOCALLY CONFORMALLY FLAT MANIFOLDS IN DIMENSIONS 4k

We give global restrictions on the possible boundaries of compact, orientable, locally conformally flat manifolds of dimension 4k in terms of integrality of eta invariants.