Search results for "Manifold"

Transitive Anosov flows and Axiom-A diffeomorphisms

2009

AbstractLet M be a smooth compact Riemannian manifold without boundary, and ϕ:M×ℝ→M a transitive Anosov flow. We prove that if the time-one map of ϕ is C1-approximated by Axiom-A diffeomorphisms with more than one attractor, then ϕ is topologically equivalent to the suspension of an Anosov diffeomorphism.

Deformations of Calabi-Yau manifolds in Fano toric varieties

2020

In this article, we investigate deformations of a Calabi-Yau manifold $Z$ in a toric variety $F$, possibly not smooth. In particular, we prove that the forgetful morphism from the Hilbert functor $H^F_Z$ of infinitesimal deformations of $Z$ in $F$ to the functor of infinitesimal deformations of $Z$ is smooth. This implies the smoothness of $H^F_Z $ at the corresponding point in the Hilbert scheme. Moreover, we give some examples and include some computations on the Hodge numbers of Calabi-Yau manifolds in Fano toric varieties.

On the Energy of Distributions, with Application to the Quaternionic Hopf Fibrations

2001

The energy of an oriented q-distribution ? in a compact oriented manifold M is defined to be the energy of the section of the Grassmannian manifold of oriented q-planes in M induced by ?. In the Grassmannian, the Sasaki metric is considered. We show here a condition for a distribution to be a critical point of the energy functional. In the spheres, we see that Hopf fibrations \(\) are critical points. Later, we prove the instability for these fibrations.

Heisenberg quasiregular ellipticity

2016

Following the Euclidean results of Varopoulos and Pankka--Rajala, we provide a necessary topological condition for a sub-Riemannian 3-manifold $M$ to admit a nonconstant quasiregular mapping from the sub-Riemannian Heisenberg group $\mathbb{H}$. As an application, we show that a link complement $S^3\backslash L$ has a sub-Riemannian metric admitting such a mapping only if $L$ is empty, the unknot or Hopf link. In the converse direction, if $L$ is empty, a specific unknot or Hopf link, we construct a quasiregular mapping from $\mathbb{H}$ to $S^3\backslash L$. The main result is obtained by translating a growth condition on $\pi_1(M)$ into the existence of a supersolution to the $4$-harmonic…

Manifolds of quasiconformal mappings and the nonlinear Beltrami equation

2014

In this paper we show that the homeomorphic solutions to each nonlinear Beltrami equation $\partial_{\bar{z}} f = \mathcal{H}(z, \partial_{z} f)$ generate a two-dimensional manifold of quasiconformal mappings $\mathcal{F}_{\mathcal{H}} \subset W^{1,2}_{\mathrm{loc}}(\mathbb{C})$. Moreover, we show that under regularity assumptions on $\mathcal{H}$, the manifold $\mathcal{F}_{\mathcal{H}}$ defines the structure function $\mathcal{H}$ uniquely.

The volume of geodesic balls and tubes about totally geodesic submanifolds in compact symmetric spaces

1997

AbstractLet M be a compact Riemannian symmetric space. We give an analytical expression for the area and volume functions of geodesic balls in M and for the area and volume functions of tubes around some totally geodesic submanifolds P of M. We plot the graphs of these functions for some compact irreducible Riemannian symmetric spaces of rank two.

Complex powers on noncompact manifolds and manifolds with singularities

1988

On the Existence and Structure of Ψ*-Algebras of Totally Characteristic Operators on Compact Manifolds with Boundary

1999

As a contribution to the pseudodifferential analysis on manifolds with singularities we construct for each smooth, compact manifold X with boundary a Ψ*-algebra A(b)∞(X, bΩ1/2)⊆L(ϱbL2(X, bΩ1/2)) containing the algebra Ψ0b, cl(X, bΩ1/2) of totally characteristic pseudodifferential operators introduced by Melrose [25] in 1981 as a dense subalgebra; further, there is a homomorphism τ(b)A: A(b)∞(X, bΩ1/2)→Q(b)Ψ characterizing the Fredholm property of a∈A(b)∞(X, bΩ1/2) by means of the invertibility of τ(b)A(a)∈Q(b)Ψ, where Q(b)Ψ is an algebra of C∞-symbols reflecting the smooth structure of the manifold X. The Fredholm inverses of Fredholm operators in A(b)∞(X, bΩ1/2) are again in the algebra A(…

Quantization on the Virasoro group

1990

The quantization of the Virasoro group is carried out by means of a previously established group approach to quantization. We explicitly work out the two-cocycles on the Virasoro group as a preliminary step. In our scheme the carrier space for all the Virasoro representations is made out of polarized functions on the group manifold. It is proved that this space does not contain null vector states, even forc≦1, although it is not irreducible. The full reduction is achieved in a striaghtforward way by just taking a well defined invariant subspace ℋ(c, h), the orbit of the enveloping algebra through the vacuum, which is irreducible for any value ofc andh. ℋ(c, h) is a proper subspace of the sp…

A criterion for homeomorphism between closed Haken manifolds

2003

In this paper we consider two connected closed Haken manifolds denoted by M^3 and N^3, with the same Gromov simplicial volume. We give a simple homological criterion to decide when a given map f: M^3-->N^3 between M^3 and N^3 can be changed by a homotopy to a homeomorphism. We then give a convenient process for constructing maps between M^3 and N^3 satisfying the homological hypothesis of the map f.