Bertrand curves in five-dimensional space

Special Bertrand Curves in semi-Euclidean space E4^2 and their Characterizations

In [14] Matsuda and Yorozu.explained that there is no special Bertrand curves in Eⁿ and they new kind of Bertrand curves called (1,3)-type Bertrand curves Euclidean space. In this paper , by using the similar methods given by Matsuda and Yorozu [14], we obtain that bitorsion of the quaternionic curve is not equal to zero in semi-Euclidean space E4^2. Obtain (N,B2) type quaternionic Bertrand cur...

Five-Dimensional Space-Times

A brane in five - dimensional Minkowski space ∗

We discuss the propagation of gravity in five-dimensional Minkowski space in the presence of a four-dimensional brane. We show that there exists a solution to the wave equation that leads to a propagator exhibiting four-dimensional behavior at low energies (long distances) with five-dimensional effects showing up as corrections at high energies (short distances). We compare our results with pro...

Holomorphic curves omitting five planes in projective space

In 1928 H. Cartan proved an extension of Montel’s normality criterion to holomorphic curves in complex projective plane P2. He also conjectured that a similar result is true for holomorphic curves in P for any n. Recently the author constructed a counterexample to this conjecture for any n ≥ 3. In this paper we show how to modify Cartan’s conjecture so that it becomes true, at least for n = 3.

some characterizations for legendre curves in the 3-dimensional sasakian space

in this paper, we give some characterizations for legendre spherical, legendre normal and legendre rectifying curves in the 3-dimensional sasakian space. furthermore, we show that legendre spherical curves are also legendre normal curves. in particular, we prove that the inverse of curvature of a legendre rectifying curve is a non-constant linear function of the arclength parameter.