Geometry Seminar: Ruled real hypersurfaces in CP^n

Fecha: 9 de abril de 2021.
Hora: 12:00 a 13:00.
Lugar: Sala virtual Contraseña: 721310.

Conferenciante: Marilena Moruz (Al.I. Cuza University of Iasi).

Resumen: 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 CP^n. In this work we are interested in the study of non-degenerate ruled real hypersurfaces in CP^n. We first define such hypersurfaces, then give basic characterizations. We also construct their parameterization. They are described as follows. Given a regular curve cin CP^n, then the family of the complete, connected, complex (n–1)-dimensional totally geodesic submanifolds orthogonal to c' and Jc', 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.