Fermi Walker Derivative Research Articles

Extended optical radial direction of optical motion with extended Darboux frame

In this paper, we derive optical conditions for extended Darboux frame to make some optical motions such as uniformly optical accelerated motion, unchanged optical direction motion, and uniformly circular optical motion by using Fermi–Walker derivative. We also construct the new optical relations between the Fermi–Walker parallel transportation and these motions in 4-space. In other words, we obtain the applied geometric optical characterization for the uniformly optical accelerated motion, unchanged optical direction motion, and uniformly optical circular motion with extended Darboux frame in 4-space.

On Fermi-Walker transformation for timelike flows in spacetime

In this manuscript, we firstly suggest different type for Fermi-Walker transportations along with flow lines of a non-vanishing vector field in Minkowski spacetime. Moreover, we construct the evolution equations of Frenet fields by Fermi-Walker derivative in Minkowski spacetime. Also, Fermi Walker parallelism is obtained the evolution equations of Frenet fields. Finally, we obtain some new results for flows by this new derivative in Minkowski spacetime.

NEW VERSION OF FERMI-WALKER DERIVATIVES ACCORDING TO THE TYPE-2 BISHOP FRAME WITH ENERGY

In this paper, we obtain the Fermi-Walker derivatives of , , magnetic curves according to the type-2 Bishop frame in the space. Moreover, we obtain the energy of the Fermi-Walker derivative of magnetic curves according to the type-2 Bishop frame in space. Finally, we have energy relations of some vector fields associated with type-2 Bishop frame in the space.

ENERGY OF THE FERMI-WALKER DERIVATIVES OF MAGNETIC CURVES ACCORDING TO THE BISHOP FRAME IN THE SPACE

Fermi-Walker derivative and the energy of magnetic curves have an important place in physics and differential geometry. In this study, we calculate the Fermi-Walker derivatives of T, N1, N2 magnetic curves according to the Bishop frame in the space. Moreover, we obtain the energy of the Fermi-Walker derivative of magnetic curves according to the Bishop frame in space. Finally, we have energy relations of some vector fields associated with Bishop frame in the space.

New Uniform Motion and Fermi–Walker Derivative of Normal Magnetic Biharmonic Particles in Heisenberg Space

In the present paper, we firstly discuss the normal biharmonic magnetic particles in the Heisenberg space. We express new uniform motions and its properties in the Heisenberg space. Moreover, we obtain a new uniform motion of Fermi–Walker derivative of normal magnetic biharmonic particles in the Heisenberg space. Finally, we investigate uniformly accelerated motion (UAM), the unchanged direction motion (UDM), and the uniformly circular motion (UCM) of the moving normal magnetic biharmonic particles in Heisenberg space.

Infinitesimal relative position vector fields for observers in a reference frame and applications to conformally stationary spacetimes

We introduce and analyze the concept of infinitesimal relative position vector field between “infinitesimally nearby” observers, showing the equivalence between different definitions. Through the Fermi–Walker derivative of infinitesimal relative position vector fields along an observer in a reference frame, we characterize spacetimes admitting an umbilic foliation. Sufficient and necessary conditions for those spacetimes to be a conformally stationary spacetime are given. Finally, the important class of cosmological models known as generalized Robertson–Walker spacetimes is characterized.

A New Version of Fermi Walker Derivative with Constant Energy for Normal Image of Slant Helix in the Lie Groups

Fermi–Walker derivative and energy of curves play an important role in sensible guidelines. In this study we formulate a new energy for Fermi–Walker (FW) derivative of normal spherical image by using FW parallelism in Lie groups. By means of innovative illustration, we get new necessary and sufficient condition for the given field to be FW parallel. We give some partial differential equations. Moreover, we have some energy construction for normal spherical image in Lie groups.

A Note on Fermi Walker Derivative with Constant Energy for Tangent Indicatrix of Slant Helix in the Lie Groups

A Note on Fermi Walker Derivative with Constant Energy for Tangent Indicatrix of Slant Helix in the Lie Groups

On the Fermi-Walker Derivative for Inextensible Flows of Normal Spherical Image

On the Fermi-Walker Derivative for Inextensible Flows of Normal Spherical Image

A New Construction of Fermi-Walker Derivative by Focal Curves According to Modified Frame

A New Construction of Fermi-Walker Derivative by Focal Curves According to Modified Frame

A modified Fermi-Walker derivative for inextensible flows of binormal spherical image

AbstractFermi-Walker derivative and biharmonic particle play an important role in skillful applications. We obtain a new characterization on binormal spherical indicatrix by using the Fermi-Walker derivative and parallelism in space. We suggest that an inextensible flow is the necessary and sufficient condition for this particle. Finally, we give some characterizations for a non-rotating frame of this binormal spherical indicatrix.

The Fermi–Walker Derivative and Non-rotating Frame in Dual Space

In this study, we defined Fermi–Walker derivative in dual space $$\mathbb {D}^3$$ . Fermi–Walker transport, non-rotating frame and Fermi–Walker termed Darboux vector by using Fermi–Walker derivative are given in dual space $$\mathbb {D}^3$$ . Being conditions of Fermi–Walker transport and non-rotating frame are investigated along any dual curve for dual Frenet frame, dual Darboux frame and dual Bishop frame.

Generalized Fermi–Walker derivative and non-rotating frame

In this paper, generalized Fermi–Walker derivative, generalized Fermi–Walker parallelism and generalized non-rotating frame concepts are given for Frenet frame, Darboux frame and Bishop frame for any curve in Euclidean space. Being generalized, non-rotating frame conditions are analyzed for each frames along the curve. Then we show that Frenet and Darboux frames are generalized non-rotating frames along all curves and also Bishop frame is generalized non-rotating frame along planar curves in Euclidean space.

Normal Fermi- Walker Derivative

In this paper, first, we defined normal Fermi-Walker derivative and applied for adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame and Darboux vector of normal Fermi-Walker derivative by using normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are researched throughout curve for Frenet frame and Adapted frame. It is shown that vector field which take part in [13] is normal FermiWalker parallel in accordance with the normal Fermi-Walker derivative along the general helix. Also, we show that the Frenet frame is normal non-rotating frame in accordance with the normal Fermi-Walker derivative. Afterwards, we testified that the adapted frame is normal non-rotating frame throughout the general helix.

The Fermi–Walker Derivative in Minkowski Space $${E_{1}^{3}}$$ E 1 3

In this study Fermi–Walker derivative, Fermi–Walker parallelism, non-rotating frame, Fermi–Walker terms Darboux vector concepts are given for Minkowski 3-space \({E_{1}^{3}}\). First, we get any spacelike curve with a spacelike or timelike principal normal and any vector field along the curve in Minkowski 3-space \({E_{1}^{3}}\). Fermi–Walker derivative and Fermi–Walker parallelism are analyzed for any spacelike curve with a spacelike or timelike principal normal in Minkowski 3-space \({E_{1}^{3}}\) and the necessary conditions to be Fermi–Walker parallel are explained. Then the necessary definitions, concepts and theorems are analyzed about Fermi–Walker derivative for any spacelike curve with a lightlike(null) principal normal. And then, in Minkowski 3-space \({E_{1}^{3}}\) Fermi–Walker derivative is analyzed for any timelike curves.

The Fermi-Walker Derivative on the Spherical Indicatrix of Spacelike Curve in Minkowski 3-Space

In this paper Fermi-Walker derivative, Fermi-Walker parallelism, non-rotating frame and Fermi-Walker terms Darboux vector concepts are given along the spherical indicatrix of a spacelike curve with a spacelike or timelike principal normal in \({E_{1}^{3}}\). First, we consider a spacelike curve in the Minkowski space and investigate the Fermi-Walker derivative along the tangent. The concepts with the Fermi-Walker derivative are analyzed along its tangent. Then, the Fermi-Walker derivative and its theorems are analyzed along the principal normal indicatrix and the binormal indicatrix of spacelike curve in \({E_{1}^{3}}\).

On the Surface the Fermi–Walker Derivative in Minkowski 3-Space

In this paper Fermi–Walker derivative and Fermi–Walker parallelism and non-rotating frame concepts are given along the curve lying on the spacelike surface and the timelike surface in Minkowski 3-space. First, we consider a curve lying on the spacelike surface and investigate the Fermi–Walker derivative along the curve. The concepts which Fermi–Walker derivative and its theorems are analyzed along the curve lying on the spacelike surface in Minkowski 3-space. And then we consider a curve lying on the timelike surface and investigate the Fermi–Walker derivative along the curve.

The Fermi-Walker Derivative on the Spherical Indicatrix of a Space Curve

In this paper Fermi-Walker derivative and Fermi-Walker parallelism and non-rotating frame concepts are given along the spherical indicatrix of a curve in E 3. First, we consider a curve in Euclid space and investigate the Fermi-Walker derivative along the tangent. The concepts which Fermi-Walker derivative are analyzed along its tangent. Then, the Fermi-Walker derivative and its theorems are analyzed along the principal normal indicatrix and the binormal indicatrix of any curve in E 3.

The Fermi–Walker Derivative on the Spherical Indicatrix of Timelike Curve in Minkowski 3-Space

The Fermi–Walker Derivative on the Spherical Indicatrix of Timelike Curve in Minkowski 3-Space

On the Fermi–Walker Derivative for Inextensible Flows

Abstract In this paper, we explicitly determine some curves corresponding to the their flows on the three-dimensional space. We construct a new characterisation for inextensible flows of curves by using the Fermi–Walker derivative and the Fermi–Walker parallelism in space. Using the Frenet frame of the given curve, we present partial differential equations. Finally, we construct the Fermi–Walker derivative in the motion of a charged particle under the action of electric and magnetic fields.