In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the …rst time in 4-dimensional Euclidean space. Then we obtain the condition for spherical curves using the parallel transport frame of them. The conditi...

in this paper, we study b-focal curves of biharmonic b -general helices according to bishop frame in the heisenberg group heis   finally, we characterize the b-focal curves of biharmonic b- general helices in terms of bishop frame in the heisenberg group heis

In this paper, we study B-focal curves of biharmonic B -general helices according to Bishop frame in the Heisenberg group Heis   Finally, we characterize the B-focal curves of biharmonic B- general helices in terms of Bishop frame in the Heisenberg group Heis        

In this work, we describe a Frenet frame in 4-dimensional Euclidean space and call as parallel transport (PTF). PTF is an alternative approach to defining moving frame. This obtained by rotating the tangent vector first binormal of unit speed curve euler angle then give curvature functions according curve. Also, introduce $(k,m)$-type slant helices 4-Space. Additionally, obtain characterization...

A recently-developed theory of quantum general relativity provides a propagator for free-falling particles in curved spacetimes. These propagators are constructed by parallel-transporting quantum states within a quantum bundle associated to the Poincaré frame bundle. We consider such parallel transport in the case that the spacetime is a classical Robertson-Walker universe. An explicit integral...

In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...