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# Ruled real hypersurfaces in $$\mathbb CP^n_p$$

## Marilena MoruzAl.I. Cuza University of Iasi

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.

# Minimal Lagrangian isotropic immersions in indefinite complex space forms

## Marilena MoruzAl.I. Cuza University of Iasi

I am interested in the study of minimal isotropic Lagrangian sub manifolds $$M^n$$ ($$n>2$$) in indefinite complex space forms. It is known that the dimension of $$M^n$$ must satisfy $$n=3r+2$$, with r a positive integer, and for $$n<14$$ there exists a classification for such submanifolds. In my work I have extended the result for an arbitrary dimension n. Therefore, I have determined all the possible dimensions of $$M^n$$ and found all the components of the second fundamental form, according to the metric with which $$M^n$$ is endowed in each case.

Seminario 2ª Planta, IEMath-GR

# Marilena Moruz

## Al.I. Cuza University of Iasi (Rumania)

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