Slant Submanifolds in Complex Euclidean Spaces - Project Euclid
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Slant Submanifolds in Complex Euclidean Spaces - Project Euclid
May 28, 1990 - $=\sum_{\sigma eS_{2n}}sign(\sigma)\Omega_{0}(e_{\sigma\langle 1)}, ... delta_{a_{1}a\{\cdots a_{n}a_{\dot{n}}}^{12\cdots\cdots(2n)}$. $\simeq ..... From (4.1), (4.16), (4.17) and (4.18) we find $(be'+2)\sin\theta=0$.
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Slant Submanifolds in Complex Euclidean Spaces Bang-Yen CHEN and Yoshihiko TAZAWA Michigan State University and Tokyo Denki University (Communicated by T. Nagano)
Abstract. An immersion of a differentiable manifold into an almost Hernitian manifold is called a 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 $C$ “ 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 when they are contained in a hypersphere , or contained in a hyperplane , or when their Gauss maps have rank $
