2021/02/21 by Marilena Moruz, Moruz, Marilena, Ortega, Miguel +2
Mathematics · #53B25 #53B30 #53C42 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2102.10641
openalex publication_date 2021/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main two families of real hypersurfaces in complex space forms are Hopf and ruled. However, very little is known about real hypersurfaces in the indefinite complex projective space \cpn. In a previous work, Kimura and the second author introduced Hopf real hypersurfaces in \cpn. In this paper, ruled real hypersurfaces in the indefinite complex projective space are introduced, as those whose maximal holomorphic distribution is integrable, and such that the leaves are totally geodesic holomorphic hyperplanes. A detailed description of the shape operator is computed, obtaining two main different families. A method of construction is exhibited, by gluing in a suitable way totally geodesic holomorphic hyperplanes along a non-null curve. Next, the classification of all minimal ruled real hypersurfaces is obtained, in terms of three main families of curves, namely geodesics, totally real circles and a third case which is not a Frenet curve, but can be explicitly computed. Four examples of minimal ruled real hypersurfaces are described.