# Geometry Seminar

#### Event Details

Date: April 9, 2021
Time: 12h-13h
Author:Marilena Moruz (Al.I. Cuza University of Iasi)
Title: Ruled real hypersurfaces in $$\mathbb CP^n_p$$
Summary: H. Anciaux and K. Panagiotidou [1] initiated the study of non-degenerate real hypersurfaces in non-flat indefinite complex space forms in 2015. Next, in 2019 M. Kimura and M. Ortega [2] further developed their ideas, with a focus on Hopf real hypersurfaces in the indefinite complex projective space $$\mathbb CP^n_p$$. In this work we are interested in the study of non-degenerate ruled real hypersurfaces in $$\mathbb CP^n_p$$. We first define such hypersurfaces, then give basic characterizations. We also construct their parameterization. They are described as follows. Given a regular curve $$\alpha$$ in $$\mathbb CP^n_p$$, then the family of the complete, connected, complex $$(n - 1)$$-dimensional totally geodesic submanifolds orthogonal to $$\alpha'$$ and $$J\alpha'$$, where $$J$$ is the complex structure, generates a ruled real hypersurface. This representation agrees with the one given by M. Lohnherr and H. Reckziegel in the Riemannian case [3]. Further insights are given into the cases when the ruled real hypersurfaces are minimal or have constant sectional curvatures. The present results are part of a joint work together with prof. M. Ortega and prof. J.D. Pérez.
[1] H. Anciaux, K. Panagiotidou, Hopf Hypersurfaces in pseudo-Riemannian complex and para-complex space forms, Diff. Geom. Appl. 42 (2015) 1-14.
[2] M. Kimura, M. Ortega, Hopf Real Hypersurfaces in Indefinite Complex Projective, Mediterr. J. Math. (2019) 16:27.
[3] M. Lohnherr, H. Reckziegel, On ruled real hypersurfaces in complex space forms. Geom. Dedicata 74 (1999), no. 3, 267–286.
Where: https://oficinavirtual.ugr.es/redes/SOR/SALVEUGR/accesosala.jsp?IDSALA=22960561