On Knotted Spheres in Euclidean $4$-space ${\mathbb{E}}^4$

Abstract

In the present study we consider knotted spheres in Euclidean $4$-space ${\mathbb{E}}^4$. Firstly, we give some basic curvature properties of knotted spheres in ${\mathbb{E}}^4$. Further, we obtained some results related with the conjugate nets and Laplace transforms of these kind of surfaces.