Abstract
Ruled real hypersurfaces in a nonflat complex space form $\tilde{M}_n(c) (n ≧ 2)$ are obtained by having a one-codimensional foliation whose leaves are totally geodesic complex hypersurfaces of the ambient space. Motivated by a fact that the sectional curvature $K$ of every ruled real hypersurface $M$ in $\tilde{M}_n(c) (n ≧ 3)$ satisfies $|c/4| ≦ |K(X,Y)| ≦ |c|$ for an arbitrary pair of orthonormal vectors $X$ and $Y$ that are tangent to the leaf at each point $x$ of $M$, we study ruled real hypersurfaces having the sectional curvature $K$ with $|c/4| ≦ |K| ≦ |c|$ in $\tilde{M}_n(c)$.
Citation
Sadahiro Maeda. Hiromasa Tanabe. Young Ho Kim. "Ruled real hypersurfaces having the same sectional curvature as that of an ambient nonflat complex space form." Kodai Math. J. 39 (1) 119 - 128, March 2016. https://doi.org/10.2996/kmj/1458651695
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