arXiv research

In this study, we consider curves of generalized AW(k)-type of Euclidean n-space. We give curvature conditions of these kind of curves.

In this study, we consider AW(k)-type curves according to the Bishop Frame in Euclidean space E^3. We give the relations between the Bishop curvatures k_1, k_2 of a curve in E^3.

In this study we consider AW(k)-type curves according to parallel transport frame in Euclidean space E^4. We give the relations between the parallel transport curvatures of these kinds of curves.

We introduce the notion of $k$-type slant helix in Minkowski space $\e_1^4$. For partially null and pseudo null curves in $\e_1^4$, we express some characterizations in terms of their curvature and torsion functions.

Study of singular foliations of b^k-type and their geometric properties.

This paper is devoted to the study of AW(k)-type curves according to the equiform differential geometry of the pseudo-Galilean space. We show that equiform Bertrand curves are circular helices or isotropic circles of the pseudo-Galilean space. Also, there are equiform Bertrand curves of AW(3) and weak AW(3)-types. More…

In this paper, we discuss the recognition problem for A_k-type singularities on wave fronts. We give computable and simple criteria of these singularities, which will play a fundamental role in generalizing the authors' previous work "the geometry of fronts" for surfaces. The crucial point to prove our criteria for A_k…

Let $G$ be a connected, linear, real reductive Lie group with compact centre. Let $K<G$ be compact. Under a condition on $K$, which holds in particular if $K$ is maximal compact, we give a geometric expression for the multiplicities of the $K$-types of any tempered representation (in fact, any standard representation) …

It is a classical result, due to F. Tricceri, that the blow-up of a manifold of locally conformally Kähler (l.c.K. for short) type at some point is again of l.c.K. type. However, the proof given in \cite{Tric} is somehow unclear. We give a different argument to prove the result, using "standard tricks" in algebraic geo…

In this study, firstly, Mannheim curves with $κ_1 (s) \ne 0$, $κ_2 (s) \ne 0$ are considered and the conditions are obtained for Mannheim curve to be slant helix. Moreover, the necessary and sufficient conditions are investigated for Mannheim curve to be AW(2), AW(3) and weak AW(2)-types, respectively. Lastly, it is sh…

We describe Lefschetz-Bott fibrations on complex line bundles over symplectic manifolds explicitly. As an application, we construct more than one strong symplectic filling of the link of the $A_{k}$-type singularity. In the appendix, we show that the total space of a Lefschetz-Bott fibration over the unit disk serves a…

Suppose $Γ$ is an arithmetic group defined over a global field $K$, that the $K$-type of $Γ$ is $A_n$ with $n \geq 2$, and that the ambient semisimple group that contains $Γ$ as a lattice has at least two noncocompact factors. We use results from Bestvina-Eskin-Wortman and Cornulier-Tessera to show that $Γ$ has a polyn…

In this paper we study the analytic realisation of the discrete series representations for the group $G=Sp(1,1)$ as a subspace of the space of square integrable sections in a homogeneous vector bundle over the symmetric space $G/K:=Sp(1,1) /(Sp(1) \times Sp(1))$. We use the Szegö map to give expressions for the restric…

The paper studies heat kernel behavior on symmetric spaces.

Let $G/K$ be a simply connected compact irreducible symmetric space of real rank one. For each $K$-type $τ$ we compare the notions of $τ$-representation equivalence with $τ$-isospectrality. We exhibit infinitely many $K$-types $τ$ so that, for arbitrary discrete subgroups $Γ$ and $Γ'$ of $G$, if the multiplicities of $…

Classifies and constructs intertwining differential operators between line and vector bundles over real projective space.

The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with respect to reductive symmetric pairs. We present a number of multiplicity-free branch…

Let $G$ be a connected, linear, real reductive Lie group with compact centre. Let $K<G$ be maximal compact. For a tempered representation $π$ of $G$, we realise the restriction $π|_K$ as the $K$-equivariant index of a Dirac operator on a homogeneous space of the form $G/H$, for a Cartan subgroup $H<G$. (The result in f…

Proves convexity of level sets of general inverse σ_k equations.

Estimates population profile from small random samples.

The paper studies multiple descent in multi-component prediction models.

Many models in mathematical physics are given as non-linear partial differential equation of hydrodynamic type; the incompressible Euler, KdV, and Camassa--Holm equations are well-studied examples.A beautiful approach to well-posedness is to go from the Eulerian to a Lagrangian description.Geometrically it corresponds …

Despite the prevalence of collaborative filtering in recommendation systems, there has been little theoretical development on why and how well it works, especially in the "online" setting, where items are recommended to users over time. We address this theoretical gap by introducing a model for online recommendation sy…