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Mahmut Ergüt

Publications and source records attributed to Mahmut Ergüt.

7 recordsLinked to original sources
arXiv2025

Constant curvature curves in dual affine and dual Lorentz-Minkowski planes

In this paper, we first study invariants of curves parametrized by a real variable in the dual plane $\mathbb{D}^2$ under equiaffine transformations. We then obtain explicit equations for all curves in $\mathbb{D}^2$ whose equiaffine curvature is a dual constant. In particular, we prove that when the equiaffine curvature is a pure real constant, both the real and dual parts of the curve in $\mathbb{D}^2$ are quadratic curves. In addition, we provide a complete classification of spacelike and timelike curves parametrized by a real variable in the dual Lorentz--Minkowski plane $\mathbb{D}^2_1$ whose curvature is a dual constant.

math.DG↗
arXiv2018

On space-like generalized constant ratio hypersufaces in Minkowski spaces

A hypersurface in a Euclidean space $\mathbb{E}^{n+1}$ is said to be a generalized constant ratio (GCR) hypersurface if the tangential part of its position vector is one of its principle directions. In this work, we move the study of generalized constant ratio hypersurfaces started in \cite% {YuFu2014GCRS} into the Minkowski space. First, we get some geometrical properties of non-degenerated GCR hypersurfaces in an arbitrary dimensional Minkowski space. Then, we obtain complete classification of GCR surfaces in the Minkowski 3-space. We also give some explicit examples.

math.DG↗
arXiv2011

Special curves of 4d galilean space

Special curves and their characterizations are one of the main area of mathematicians and physicians. As a special curve we will mainly focus on Mannheim curve which has the following relation: k1=β(k1^2+k2^) where k1 and k2 are curvature and torsion, respectively. In the present paper we define Mannheim curves for 4-dimensional Galilean space and investigate some characterization of it.

math.DG↗