Ch flat curves in Euclidean space $E^{2n+1}$

Lj. Protić; N. Bokan

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Displaying similar documents to “Ch flat curves in Euclidean space $E^{2 n + 1}$ ”

A topological application of flat morasses

R. W. Knight (2007)

Fundamenta Mathematicae

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We define combinatorial structures which we refer to as flat morasses, and use them to construct a Lindelöf space with points $G_{δ}$ of cardinality $ℵ_{ω}$ , consistent with GCH. The construction reveals, it is hoped, that flat morasses are a tool worth adding to the kit of any user of set theory.

Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree

Nazar Arakelian, Herivelto Borges (2015)

Acta Arithmetica

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For each integer s ≥ 1, we present a family of curves that are $_{q}$ -Frobenius nonclassical with respect to the linear system of plane curves of degree s. In the case s=2, we give necessary and sufficient conditions for such curves to be $_{q}$ -Frobenius nonclassical with respect to the linear system of conics. In the $_{q}$ -Frobenius nonclassical cases, we determine the exact number of $_{q}$ -rational points. In the remaining cases, an upper bound for the number of $_{q}$ -rational points will follow from Stöhr-Voloch...

Remarks on flat and differential $K$ -theory

Man-Ho Ho (2014)

Annales mathématiques Blaise Pascal

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In this note we prove some results in flat and differential $K$ -theory. The first one is a proof of the compatibility of the differential topological index and the flat topological index by a direct computation. The second one is the explicit isomorphisms between Bunke-Schick differential $K$ -theory and Freed-Lott differential $K$ -theory.

An index inequality for embedded pseudoholomorphic curves in symplectizations

Michael Hutchings (2002)

Journal of the European Mathematical Society

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Let $Σ$ be a surface with a symplectic form, let $φ$ be a symplectomorphism of $Σ$ , and let $Y$ be the mapping torus of $φ$ . We show that the dimensions of moduli spaces of embedded pseudoholomorphic curves in $ℝ \times 𝕐$ , with cylindrical ends asymptotic to periodic orbits of $φ$ or multiple covers thereof, are bounded from above by an additive relative index. We deduce some compactness results for these moduli spaces. This paper establishes some of the foundations for a program with Michael Thaddeus, to...

Some results on $G_{C}$ -flat dimension of modules

Ramalingam Udhayakumar, Intan Muchtadi-Alamsyah, Chelliah Selvaraj (2019)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we study some properties of $G_{C}$ -flat $R$ -modules, where $C$ is a semidualizing module over a commutative ring $R$ and we investigate the relation between the $G_{C}$ -yoke with the $C$ -yoke of a module as well as the relation between the $G_{C}$ -flat resolution and the flat resolution of a module over $G F$ -closed rings. We also obtain a criterion for computing the $G_{C}$ -flat dimension of modules.

Complete pluripolar curves and graphs

Tomas Edlund (2004)

Annales Polonici Mathematici

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It is shown that there exist $C^{\infty}$ functions on the boundary of the unit disk whose graphs are complete pluripolar. Moreover, for any natural number k, such functions are dense in the space of $C^{k}$ functions on the boundary of the unit disk. We show that this result implies that the complete pluripolar closed $C^{\infty}$ curves are dense in the space of closed $C^{k}$ curves in ℂⁿ. We also show that on each closed subset of the complex plane there is a continuous function whose graph is complete pluripolar. ...

Rational points on $X_{0}^{+} (p^{r})$

Yuri Bilu, Pierre Parent, Marusia Rebolledo (2013)

Annales de l’institut Fourier

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Using the recent isogeny bounds due to Gaudron and Rémond we obtain the triviality of $X_{0}^{+} (p^{r}) (ℚ)$ , for $r > 1$ and $p$ a prime number exceeding $2 \cdot 10^{11}$ . This includes the case of the curves $X_{split} (p)$ . We then prove, with the help of computer calculations, that the same holds true for $p$ in the range $11 \leq p \leq 10^{14}$ , $p \neq 13$ . The combination of those results completes the qualitative study of rational points on $X_{0}^{+} (p^{r})$ undertook in our previous work, with the only exception of $p^{r} = 13^{2}$ .

Special sets of reals and weak forms of normality on Isbell--Mrówka spaces

Vinicius de Oliveira Rodrigues, Victor dos Santos Ronchim, Paul J. Szeptycki (2023)

Commentationes Mathematicae Universitatis Carolinae

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We recall some classical results relating normality and some natural weakenings of normality in $Ψ$ -spaces over almost disjoint families of branches in the Cantor tree to special sets of reals like $Q$ -sets, $λ$ -sets and $σ$ -sets. We introduce a new class of special sets of reals which corresponds to the corresponding almost disjoint family of branches being $ℵ_{0}$ -separated. This new class fits between $λ$ -sets and perfectly meager sets. We also discuss conditions for an almost disjoint family $𝒜$ being...

On invariants of elliptic curves on average

Amir Akbary, Adam Tyler Felix (2015)

Acta Arithmetica

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We prove several results regarding some invariants of elliptic curves on average over the family of all elliptic curves inside a box of sides A and B. As an example, let E be an elliptic curve defined over ℚ and p be a prime of good reduction for E. Let $e_{E} (p)$ be the exponent of the group of rational points of the reduction modulo p of E over the finite field $_{p}$ . Let be the family of elliptic curves $E_{a, b} : y^{2} = x^{3} + a x + b$ , where |a| ≤ A and |b| ≤ B. We prove that, for any c > 1 and k∈ ℕ, $1 / | | \sum_{E \in} \sum_{p \leq x} e_{E}^{k} (p) = C_{k} l i (x^{k + 1}) + O ((x^{k + 1}) / {(l o g x)}^{c}$ )as x → ∞, as long...

On ramified covers of the projective plane II: Generalizing Segre’s theory

Michael Friedman, Rebecca Lehman, Maxim Leyenson, Mina Teicher (2012)

Journal of the European Mathematical Society

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The classical Segre theory gives a necessary and sufficient condition for a plane curve to be a branch curve of a (generic) projection of a smooth surface in $ℙ^{3}$ . We generalize this result for smooth surfaces in a projective space of any dimension in the following way: given two plane curves, $B$ and $E$ , we give a necessary and sufficient condition for $B$ to be the branch curve of a surface $X$ in $ℙ^{N}$ and $E$ to be the image of the double curve of a $ℙ^{3}$ -model of $X$ . In the classical Segre theory, a...

Quantum Singularity Theory for $A_{(r - 1)}$ and $r$ -Spin Theory

Huijun Fan, Tyler Jarvis, Yongbin Ruan (2011)

Annales de l’institut Fourier

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We give a review of our construction of a cohomological field theory for quasi-homogeneous singularities and the $r$ -spin theory of Jarvis-Kimura-Vaintrob. We further prove that for a singularity $W$ of type $A$ our construction of the stack of $W$ -curves is canonically isomorphic to the stack of $r$ -spin curves described by Abramovich and Jarvis. We further prove that our theory satisfies all the Jarvis-Kimura-Vaintrob axioms for an $r$ -spin virtual class. Therefore, the Faber-Shadrin-Zvonkine...

Asymmetric tie-points and almost clopen subsets of $ℕ^{*}$

Alan S. Dow, Saharon Shelah (2018)

Commentationes Mathematicae Universitatis Carolinae

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A tie-point of compact space is analogous to a cut-point: the complement of the point falls apart into two relatively clopen non-compact subsets. We review some of the many consistency results that have depended on the construction of tie-points of $ℕ^{*}$ . One especially important application, due to Veličković, was to the existence of nontrivial involutions on $ℕ^{*}$ . A tie-point of $ℕ^{*}$ has been called symmetric if it is the unique fixed point of an involution. We define the notion of an almost...

Explicit Teichmüller curves with complementary series

Carlos Matheus, Gabriela Weitze-Schmithüsen (2013)

Bulletin de la Société Mathématique de France

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We construct an explicit family of arithmetic Teichmüller curves $𝒞_{2 k}$ , $k \in ℕ$ , supporting $SL (2, ℝ)$ -invariant probabilities $μ_{2 k}$ such that the associated $SL (2, ℝ)$ -representation on $L^{2} (𝒞_{2 k}, μ_{2 k})$ has complementary series for every $k \geq 3$ . Actually, the size of the spectral gap along this family goes to zero. In particular, the Teichmüller geodesic flow restricted to these explicit arithmetic Teichmüller curves $𝒞_{2 k}$ has arbitrarily slow rate of exponential mixing.

Local equivalence of some maximally symmetric $(2, 3, 5)$ -distributions II

Matthew Randall (2025)

Archivum Mathematicum

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We show the change of coordinates that maps the maximally symmetric $(2, 3, 5)$ -distribution given by solutions to the $k = \frac{2}{3}$ and $k = \frac{3}{2}$ generalised Chazy equation to the flat Cartan distribution. This establishes the local equivalence between the maximally symmetric $k = \frac{2}{3}$ and $k = \frac{3}{2}$ generalised Chazy distribution and the flat Cartan or Hilbert-Cartan distribution. We give the set of vector fields parametrised by solutions to the $k = \frac{2}{3}$ and $k = \frac{3}{2}$ generalised Chazy equation and the corresponding Ricci-flat conformal scale...

On covering and quasi-unsplit families of curves

Laurent Bonavero, Cinzia Casagrande, Stéphane Druel (2007)

Journal of the European Mathematical Society

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Given a covering family $V$ of effective 1-cycles on a complex projective variety $X$ , we find conditions allowing one to construct a geometric quotient $q : X \to Y$ , with $q$ regular on the whole of $X$ , such that every fiber of $q$ is an equivalence class for the equivalence relation naturally defined by $V$ . Among other results, we show that on a normal and $ℚ$ -factorial projective variety $X$ with canonical singularities and $dim X \leq 4$ , every covering and quasi-unsplit family $V$ of rational curves generates a geometric...

Shells of monotone curves

Josef Mikeš, Karl Strambach (2015)

Czechoslovak Mathematical Journal

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We determine in $ℝ^{n}$ the form of curves $C$ corresponding to strictly monotone functions as well as the components of affine connections $\nabla$ for which any image of $C$ under a compact-free group $Ω$ of affinities containing the translation group is a geodesic with respect to $\nabla$ . Special attention is paid to the case that $Ω$ contains many dilatations or that $C$ is a curve in $ℝ^{3}$ . If $C$ is a curve in $ℝ^{3}$ and $Ω$ is the translation group then we calculate not only the components of the curvature and the Weyl...

Displaying similar documents to “Ch flat curves in Euclidean space E 2 n + 1 ”

Displaying similar documents to “Ch flat curves in Euclidean space $E^{2 n + 1}$ ”