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Konstantina Panagiotidou

Publications and source records attributed to Konstantina Panagiotidou.

5 recordsLinked to original sources
arXiv2016

Nullity distributions on real hypersurfaces in non-flat complex space forms

In this paper the result of real hypersurfaces in non-flat complex space forms, whose structure vector field $ξ$ belongs to the $κ$-nullity distribution is extended in case of three dimensional real hypersurfaces in non-flat complex space forms. Furthermore, generalization of notion ($κ$,$μ$)-nullity distribution defined on real hypersurfaces and results of real hypersurfaces, whose structure vector field $ξ$ belongs to the previous distribution are provided. Finally, the notion of ($κ$,$μ$,$ν$)-nullity distribution is introduced in case of real hypersurfaces in non-flat complex space forms and real hypersurfaces, whose structure vector field $ξ$ belongs to the previous distribution are studied.

math.DG↗
arXiv2016

Conditions of parallelism of *-Ricci tensor of three dimensional real hypersurfaces in non-flat complex space forms

This paper focuses on the study of three dimensional real hypersurfaces in non-flat complex space forms whose $^{*}$-Ricci tensor satisfies conditions of parallelism. More precisely, extension of existing results concerning real hypersurfaces with vanishing, semi-parallel and pseudo-parallel $^{*}$-Ricci tensor in case of ambient space being the complex hyperbolic space are provided. Furthermore, new results concerning $ξ$-parallelism of $^{*}$-Ricci tensor of real hypersurfaces in non-flat complex space forms are presented.

math.DG↗
arXiv2014

Hopf Hypersurfaces in pseudo-Riemannian complex and para-complex space forms

The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by $J$ be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field $N$ is said to be \em Hopf \em if the tangent vector field $JN$ is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the \em Hopf \em curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel.

math.DG↗
arXiv2012

Semi-parallelism of normal Jacobi operator for Hopf hypersurfaces in complex two-plane Grassmannians

It is proved the non-existence of Hopf hypersurfaces in $G_{2}({\Bbb C}^{m+2})$, $m \geq 3$, whose normal Jacobi operator is semi-parallel, if the principal curvature of the Reeb vector field is non-vanishing and the component of the Reeb vector field in the maximal quaternionic subbundle ${\frak D}$ or its orthogonal complement ${\frak D}^{\bot}$ is invariant by the shape operator.

math.DG↗