Heisenberg Group Heis3 Research Articles

Inextensible flows of biharmonic S-curves according to Sabban frame in Heisenberg group Heis3

In this work, we examine inextensible flows associated biharmonic curves depending to Sabban frame in Heis3. We define the biharmonic curves with regards to their curvatures. The differential equations characterizing biharmonic curves are given in Heis3. Additionaly, we discover equations of one parameter family of biharmonic curves in .

Biharmonic constant Π₁-slope curves according to type-2 bishop frame in Heisenberg group Heis³

In this paper, we introduce constant Π₁- slope curves according to type-2 Bishop frame in the Heisenberg group Heis³. We characterize the biharmonic constant Π₁- slope curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric equations in the Heisenberg group Heis³. Additionally, we illustrate our main theorem.

PEDAL CURVES OF TANGENT SURFACES OF BIHARMONIC B-GENERAL HELICES ACCORDING TO BISHOP FRAME IN HEISENBERG GROUP Heis³

In this paper, we study pedal curves of tangent surfaces of biharmonic B-general helices according to Bishop frame in the Heisenberg group Heis³. We give necessary and sufficient conditions for B-general helices to be biharmonic according to Bishop frame. We characterize this pedal curves in the Heisenberg group Heis³. Additionally, we illustrate our main theorem.

BISHOP EQUATIONS OF SMARANDACHE TM₁ CURVES OF BIHARMONIC B-SLANT HELICES IN Heis³

In this paper, we study Bishop equations for Smarandache TM₁ curves of biharmonic B-slant helices according to Bishop frame in the Heisenberg group Heis³. Finally, we characterize the Smarandache TM₁ curves of biharmonic B-slant helices in terms of Bishop frame in the Heisenberg group Heis³.

Tangent Surfaces of Biharmonic B-General Helices According to Bishop Frame in Heisenberg Group Heis3

Tangent Surfaces of Biharmonic B-General Helices According to Bishop Frame in Heisenberg Group Heis3

Construction of Focal Curves of Spacelike 0-Biharmonic Curves with Timelike Binormal in the Lorentzian Heisenberg Group Heis3

In this paper, we study focal curve of spacelike biharmonic curve with a timelike binormal in the Heis 3 . We characterize focal curve of spacelike biharmonic curve with a timelike binormal in terms of curvature and torsion of biharmonic curve in the Heis . 3 Finally, we construct parametric equations of focal curve of spacelike biharmonic curve with a timelike binormal curve.

Tubular Surfaces Around Timelike Biharmonic Curves in Lorentzian Heisenberg Group Heis3

Abstract In this paper, we describe a new method for constructing a tubular surface surrounding a timelike biharmonic curve in the Lorentzian Heisenberg group Heis3. Firstly, we characterize timelike biharmonic curves in terms of their curvature and torsion. Also, by using timelike biharmonic curves, we give explicit parametrizations of tubular surfaces in the Lorentzian Heisenberg group Heis3.

Biharmonic S-curves according to Sabban frame in Heisenberg group Heis³

In this paper, we study biharmonic curves accordig to Sabban frame in the Heisenberg group Heis³. We characterize the biharmonic curves in terms of their geodesic curvature and we prove that all of biharmonic curves are helices in the Heisenberg group Heis³. Finally, we find out their explicit parametric equations according to Sabban Frame.

<b>CHARACTERIZATION OF SPACELIKE BIHARMONIC CURVES WITH TIMELIKE BINORMAL ACCORDING TO FLAT METRIC IN LORENTZIAN HEISENBERG GROUP Heis³</b> - doi: 10.5269/bspm.v30i2.14706

In this paper, we study spacelike biharmonic curves with timelike binormal according to flat metric in the Lorentzian Heisenberg group Heis³. We characterize spacelike biharmonic curves with timelike binormal in terms of their curvature and torsion. Additionally, we determine the parametric representation of the spacelike biharmonic curves with timelike binormal according to flat metric from this characterization.

On Characterization Canal Surfaces around Timelike Horizontal Biharmonic Curves in Lorentzian Heisenberg Group Heis3

In this paper, we describe a new method for constructing a canal surface surrounding a timelike horizontal biharmonic curve in the Lorentzian Heisenberg group Heis3. Firstly, we characterize timelike biharmonic curves in terms of their curvature and torsion. Also, by using timelike horizontal biharmonic curves, we give explicit parametrizations of canal surfaces in the Lorentzian Heisenberg group Heis3

On Characterization of Time-Like Horizontal Biharmonic Curves in the Lorentzian Heisenberg Group Heis3

In this paper, we study energy of time-like horizontal biharmonic curves in the Lorentzian Heisenberg group Heis3. We characterize the biharmonic curves in terms of their curvature and torsion. We prove that all of the biharmonic curves are helices. Finally, we study the mechanics of biharmonic curves and provide conditions for energy of horizontal biharmonic curves