Regular subspaces of a quaternionic Hilbert space from quaternionic Hermite polynomials and associated coherent states

We define quaternionic Hermite polynomials by analogy with two families of complex Hermite polynomials. As in the complex case, these polynomials consatitute orthogonal families of vectors in ambient quaternionic $L^2$-spaces. Using these polynomials, we then define regular and anti-regular subspaces of these $L^2$-spaces, the associated reproducing kernels and the ensuing quaternionic coherent states

The slant helices according to Bishop frame of the spacelike curve in Lorentzian space

T. Ikawa obtained the following differential equation DTDTDTT-KDTT, K = k2 - r2 for the circular helix which corresponds the case that the curvature k and torsion ? of spacelike curve with a spacelike binormal ? on the Lorentzian manifold M1 are constant [7]. In this paper, we have defined a slant helix according to Bishop frame of the spacelike curve with a spacelike binormal. Furthermore, we have given some necessary and sufficient conditions for the slant helix and T. Ikawa's result is generalized to the case of the general slant helix. © Taru Publications