The theory of finite type submanifolds was introduced by the first author in late 1970s and it
has become a useful tool for investigation of submanifolds. Later, the first author and P …

We consider the birotational hypersurface $\mathbf {x (} u, v, w\mathbf {)} $ with the second
Laplace-Beltrami operator in the four dimensional Euclidean space ${\mathbb {E}}^{4}. $ We …

We study curvature formulas and the fourth fundamental form IV of hypersurfaces in the four
dimensional Euclidean geometry\(\mathbb {E}^ 4\). We calculate fourth fundamental form …

We introduce the bi-rotational hypersurface $\mathbf {x (} u, v, w\mathbf {)} $ in the four
dimensional Euclidean geometry ${\mathbb {E}}^{4}. $ We obtain the $ i $-th curvatures of …

In this paper, we study spacelike rotational surfaces which are called boost invariant
surfaces in Minkowski 4-space E41. We give necessary and sufficient condition for flat …

We examine the bi-rotational hypersurface x= x (u, v, w) with the third Laplace-Beltrami
operator in the four dimensional Euclidean space 𝔼 4. Giving the i-th curvatures of the …

HYPERSPHERE SATISFYING Ax =Ax IN 4-SPACE Page 1 Palestine Journal of
Mathematics Vol. 11(3)(2022) , 21–30 © Palestine Polytechnic University-PPU 2022 …

We introduce the timelike rotational hypersurfaces $\textbf {x} $ with timelike axis in
Minkowski 4-space $\mathbb {E} _1^{4} $. We obtain the equations for the curvatures of the …

We introduce fourth fundamental form IV, and i-th curvature formulas of hypersurfaces in the
four dimensional Euclidean geometry E 4. Defining fourth fundamental form and i-th …

In this paper, we study a class of spacelike rotational surfaces in the Minkowski 4-space
$\mathbb {E}^ 4_1 $ with meridian curves lying in 2-dimensional spacelike planes and …