## Tokyo Journal of Mathematics

### Slant Submanifolds in Complex Euclidean Spaces

#### Abstract

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

#### Article information

Source
Tokyo J. of Math. Volume 14, Number 1 (1991), 101-120.

Dates
First available in Project Euclid: 1 April 2010

http://projecteuclid.org/euclid.tjm/1270130492

Digital Object Identifier
doi:10.3836/tjm/1270130492

Mathematical Reviews number (MathSciNet)
MR1108159

Zentralblatt MATH identifier
0735.53040

#### Citation

CHEN, Bang-Yen; TAZAWA, Yoshihiko. Slant Submanifolds in Complex Euclidean Spaces. Tokyo J. of Math. 14 (1991), no. 1, 101--120. doi:10.3836/tjm/1270130492. http://projecteuclid.org/euclid.tjm/1270130492.