unique real number ϕ ( X, Y ) between 0 and π such that the Lorentzian spacelike angle between X and Y is defined to be ϕ ( X, Y ) [8]. Let X and Y be spacelike vectors in R 3 1 that span a timelike vector subspace. Then we have Hence, there is a unique positive real number ϕ ( X, Y ) between 0 and π such that the Lorentzian timelike angle between X and Y is defined to be ϕ ( X, Y ) [8]. Let X be a spacelike vector and Y be a positive timelike vector in R 3 $_{1}$. Then there is a unique nonnegative real number ϕ ( X, Y ) such that the Lorentzian timelike angle between X and Y is defined to be ϕ ( X, Y ) [8]. Let M be a semi-Riemannian submanifold of M and D be the Levi-Civita connection of M, the function II : χ ( M ) × χ ( M ) −→ χ ( M $_{)}$⊥ such that is ℑ ( M ) − bilinear and symmetric. II is callled the shape tensor (or second fundamental form tensor) of M ⊂ M [5]. Let N be a unit normal vector field on a semi-Riemannian hypersurface 5 |〈 X, Y 〉| = ‖ X ‖ ‖ Y ‖ sinh ϕ ( X, Y ) II ( X, Y ) = norD$_{X}$Y |〈 X, Y 〉| = ‖ X ‖ ‖ Y ‖ cosh ϕ ( X, Y ) |〈 X, Y 〉| > ‖ X ‖ ‖ Y ‖ . 〈 X, Y 〉 = ‖ X ‖ ‖ Y ‖ cos ϕ ( X, Y )