arXiv subjects

M. Tosun

Publications and source records attributed to M. Tosun.

7 recordsLinked to original sources

arXiv2017

Triple Root Systems, Quasi-determinantal Quivers and Linear Free Divisors

We start by constructing a new root system for rational triple singularities and determine the number of roots for each rational triple singularity. Then we show that, for each root, we obtain a linear free divisor. So we obtain a new family of linear free divisors. This gives the converse part of an existing theorem which says, by using the quiver representation, that linear free divisors come from a tree. We prove that our construction is independent of the orientation on the rational triple trees. Furthermore, we deduce that linear free divisors defined by rational triple quivers satisfy the logarithmic comparison theorem. In last section, we generalize the results of these results to rational quasi-determinantal singularities.

math.AG↗

arXiv2012

A new construction of $\tilde{D}_5$-singularities and generalization of Slodowy slices

Any simple elliptic singularity of type $\tilde{D}_5$ can be obtained by taking the intersection of the nilpotent variety and the 4-dimensional "good slices" in the semi-simple Lie algebra ${\frak sl}(2, {\mathbb C}) \oplus {\frak sl}(2, {\mathbb C})$. We describe these new slices purely by the structure of the Lie algebra. We also construct the semi-universal deformation spaces of $\tilde{D}_5$-singularities by using the 4-dimensional "good slices".

math.AG↗

arXiv2011

Generalized Timelike Mannheim Curves in Minkowski space-time $E_1^4$

We give a definition of generalized timelike Mannheim curve in Minkowski space-time $E_1^4$. The necessary and sufficient conditions for the generalized timelike Mannheim curve obtain. We show some characterizations of generalized Mannheim curve.

math.DG↗

arXiv2010

A Note an Admissible Mannheim Curves in Galilean Space

The aim of this paper is to study the Mannheim partner curves in three dimensional Galilean space . Some well known theorems are obtained related to Mannheim curves.

math.DG↗

arXiv2010

Admissible Mannheim Curves in Pseudo-Galilean Space $G_3^1$

In this paper, first and second type admissible Mannheim partner curves are defined in pseudo-Galilean space $G_3^1$. Moreover, it is proved that the distance between the reciprocal points of both of first and second type admissible Mannheim curves and the torsions of these curves are constant. Furthermore, the relations for curvatures and torsions of these curves and Schell Theorem are obtained. Finally, a result about these curves being general helix is given.

math.DG↗

arXiv2010

A Study on Dual Mannheim Partner Curves

Mannheim partner curves are studied by Liu and Wang [1,2]. Orbay and others extended the theory of the Mannheim curves to the ruled surface in Euclidean 3-space[3]. We obtain the relationships between the curvatures and the torsions of the dual Mannheim partner curves with respect to each other.

math.DG↗

arXiv2009

Invariants of open books of links of surface singularities

In the present article we determine and characterize completely the support genus, the binding number and the norm of a page of an open book under the following restrictions: M is a rational homology sphere which can be realized as the link of a surface singularity. Moreover, we restrict ourselves to the collection of those open book decompositions which can be realized as Milnor fibrations determined by some analytic germ (the so-called Milnor open books).

math.AG↗