6 citations · 33 across the 39 of their papers we have counts for
44 papers
Curvatures of curves in endowed with a canonical linear connection
Muhittin Evren Aydın, Rafael López
We investigate the geometry of plane curves in endowed with a canonical linear connection. By introducing the notions of the tangential and geodesic curvatures, we p…
Prescribed Angle Surfaces Associated with Torse-Forming Vector Fields in Riemannian Manifolds
Muhittin Evren Aydın, Esra Dilmen, Büşra Karakaya
In this paper, we introduce the notion of a prescribed angle hypersurface in a Riemannian manifold associated with a pair , where is a unit vector fi…
Curves in Riemannian Manifolds Making Prescribed Angles With Torse-Forming Vector Fields
Muhittin Evren Aydin, Esra Dilmen, Busra Karakaya
In this paper, we introduce the notion of a prescribed angle curve in a Riemannian manifold associated with a pair , where is a unit vector field alo…
Generalization of the catenary in the dual plane
Muhittin Evren Aydin, Rafael López
In this paper, we study a dual analogue of the classical catenary within the class of admissible curves in the dual plane . We introduce -catenaries in $\mathbb{D}…
Constant curvature curves in dual affine and dual Lorentz-Minkowski planes
Muhittin Evren Aydın, Nursemin Çavdar, Mahmut Ergüt
In this paper, we first study invariants of curves parametrized by a real variable in the dual plane under equiaffine transformations. We then obtain explicit equati…
Hypersurfaces in Riemannian manifolds with torse-forming axes
Muhittin Evren Aydın, Adela Mihai, Cihan Özgür
In this paper, we study orientable hypersurfaces in Riemannian manifolds for which the inner product is constant, where…
Extension of a problem of Euler in and in
Muhittin Evren Aydin, Antonio Bueno, Rafael López
In this paper, we extend the notion of stationary curves with respect to the moment of inertia from a point in the Euclidean plane to the case that the ambient s…
Invariant -translators for the Gauss curvature flow in Euclidean space
Muhittin Evren Aydin, Rafael López
A -translator is a surface in Euclidean space whose Gauss curvature satisfies , where is the Gauss map, is a fi…
Classification of ruled surfaces in Lorentz-Minkowski space that are stationary for the moment of inertia
Muhittin Evren Aydin, Rafael López
In this paper, we study hypersurfaces in Lorentz-Minkowski space that are stationary for the moment of inertia with respect to the origin. After giving examples…
Extension of a problem of Euler in Lorentz-Minkowski plane
Muhittin Evren Aydin, Rafael López
In this paper we study curves in Lorentz-Minkowski space that are critical points of the moment of inertia with respect to the origin. This extends a problem posed b…
Anti-torqued slant helices and Torqued Curves in Riemannian manifolds
Muhittin Evren Aydin, Adela Mihai, Cihan Özgür
In this paper, we introduce the notion of an anti-torqued slant helix in a Riemannian manifold, defined as a curve whose principal vector field makes a constant angle with an anti-…
Torqued and Anti-Torqued Vector Fields on Hyperbolic Spaces
Muhittin Evren Aydin, Adela Mihai, Cihan Özgür
In this paper, we study the existence of torqued and anti-torqued vector fields on the hyperbolic ambient space . Although there are examples of proper torqued vector…
Constant sectional curvature surfaces with a semi-symmetric non-metric connection
Muhittin Evren Aydin, Rafael López, Adela Mihai
Consider the Euclidean space endowed with a canonical semi-symmetric non-metric connection determined by a vector field . We…
Classification of translation surfaces in with constant sectional curvature
Muhittin Evren Aydin, Rafael López, Adela Mihai
In this paper, we study translation surfaces in the Euclidean space endowed with a canonical semi-symmetric non-metric connection. We completely classify the translation surfaces o…
Rectifying submanifolds of Riemannian manifolds with anti-torqued axis
Muhittin Evren Aydin, Adela Mihai, Cihan Özgür
In this paper we study rectifying submanifolds of a Riemannian manifold endowed with an anti-torqued vector field. For this, we first determine a necessary and sufficient condition…
Classification of separable hypersurfaces with constant sectional curvature
Muhittin Evren Aydin, Rafael Lopez, Gabriel-Eduard Vilcu
In this paper, we give a full classification of the separable hypersurfaces of constant sectional curvature in the Euclidean -space . In dimension , this clas…
Singular Miminal Ruled Surfaces
Muhittin Evren Aydin, Ayla Erdur Kara
In this paper we study surfaces with minimal potential energy under gravitational forces, called singular minimal surfaces. We prove that a singular minimal ruled surface in a Eucl…
A non-Newtonian approach in differential geometry of curves: multiplicative rectifying curves
Muhittin Evren Aydin, Aykut Has, Beyhan Yilmaz
In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension 3, i.e., those curves for which the position vector always lies in its rectifying plane…
Effect of local fractional derivatives on Riemann curvature tensor
Muhittin Evren Aydin
In this short note, we investigate the effect of the local fractional derivatives on the Riemann curvature tensor that is a common tool in calculating curvature of a Riemannian man…
Rotational -translators in Minkowski space
Muhittin Evren Aydin, Rafael López
A spacelike surface in Minkowski space is called a -translator of the flow by the powers of Gauss curvature if satisfies , $α\n…
Translators of the Gauss curvature flow
Muhittin Evren Aydin, Rafael López
A -translator is a surface in Euclidean space $\r^3$ that moves by translations in a spatial direction and under the -flow, where is the Gauss curvature and is a…
Ruled translating solitons in Minkowski 3-space
Muhittin Evren Aydin, Rafael Lopez
We characterize all ruled translating solitons in Minkowski 3-space. In contrast to the Euclidean space, we find ruled translating solitons that are not cylindrical. These surfaces…
Translating solitons of translation and homothetical types
Muhittin Evren Aydin, Rafael Lopez
We prove that if a translating soliton can be expressed as the sum of two curves and one of these curves is planar, then the other curve is also planar and consequently the surface…
Singular minimal surfaces which are minimal
Muhittin Evren Aydin, Ayla Erdur, Mahmut Ergut
In the present paper, we discuss the singular minimal surfaces in a Euclidean 3-space R^{3} which are minimal. In fact, such a surface is nothing but a plane, a trivial outcome. Ho…