Search results for " mani"

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.

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…

Complex powers on noncompact manifolds and manifolds with singularities

1988

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.

Some remarks concerning Nambu mechanics

1996

The structure of Nambu-Poisson brackets is studied and we establish that any Nambu tensor is decomposable. We show that every Nambu-Poisson manifold admits a local foliation by canonical Nambu-Poisson manifolds. Finally, a cohomology for Nambu (Lie) algebras which is adapted to the study of formal deformations of Nambu structures is introduced.

Non-immersion theorem for a class of hyperbolic manifolds

1998

Abstract It is proved that a non-simply-connected complete hyperbolic manifold cannot be isometrically immersed in a Euclidean space with a flat normal connection. In particular, the complete hyperbolic manifold M n with π 1 ( M ) ≠ 0 cannot be isometrically immersed in R 2 n − 1 .

Comparison theorems for the volume of a complex submanifold of a Kaehler manifold

1990

LetM be a Kaehler manifold of real dimension 2n with holomorphic sectional curvatureK H≥4λ and antiholomorphic Ricci curvatureρ A≥(2n−2)λ, andP is a complex hypersurface. We give a bound for the quotient (volume ofP)/(volume ofM) and prove that this bound is attained if and only ifP=C P n−1(λ) andM=C P n(λ). Moreover, we give some results on the volume of of tubes aboutP inM.

On the index form of a geodesic in a pseudoriemannian almost-product manifold

1986

Stability of the fixed point property in Hilbert spaces

2005

In this paper we prove that if X X is a Banach space whose Banach-Mazur distance to a Hilbert space is less than 5 + 17 2 \sqrt {\frac {5+\sqrt {17}}{2}} , then X X has the fixed point property for nonexpansive mappings.

On the Rational Homogeneous Manifold Structure of the Similarity Orbits of Jordan Elements in Operator Algebras

1991

Considering a topological algebra B with unit e, an open group of invertible elements B −1 and continuous inversion (e. g. B = Banach algebra, B = C∞(Ω, M n (ℂ)) (Ω smooth manifold), B = special algebras of pseudo-differential operators), we are going to define the set of Jordan elements J ⊂ B (such that J = Set of Jordan operators if B = L(H), H Hilbert space) and to construct rational local cross sections for the operation mapping $$ {B^{ - 1}} \mathrel\backepsilon g \mapsto gJ{g^{ - 1}} $$ of B −1 on the similarity orbit S(J):= {gJg −1: g Є B −1}, J Є J.