Slant Submanifolds in Complex Euclidean Spaces

An immersion of a differentiable manifold into an almost Hermitian manifold is called a slant immersion if it has constant Wirtinger angle ([3, 6]). general slant immersion which is neither holomorphic nor totally real is called a proper slant immersion. the first part of this article, we prove that every general slant immersion of a compact manifold into the complex Euclidean m-space ᵐ is totally real. result generalizes the well-known fact that there exist no compact holomorphic submanifolds in any complex Euclidean space. the second part, we classify proper slant surfaces in ² when they are contained in a hypersphere S³, or contained in a hyperplane E³, or when their Gauss maps have rank $<2$.