Departamento de Geometría y Topología
https://hdl.handle.net/10481/29854
2024-03-29T06:30:37ZThe geodesic completeness of compact Lorentzian manifolds admitting a timelike Killing vector field revisited: two new proofs
https://hdl.handle.net/10481/90082
The geodesic completeness of compact Lorentzian manifolds admitting a timelike Killing vector field revisited: two new proofs
Fuente Benito, Daniel de la
Compact Lorentzian manifolds admitting a timelike Killing vector
field are shown to be complete by means of two different proofs to the original
one.
Spacelike surfaces which admit a nondegenerate null normal section in a Lorentzian space form
https://hdl.handle.net/10481/90079
Spacelike surfaces which admit a nondegenerate null normal section in a Lorentzian space form
Fuente Benito, Daniel de la; Palomo, Francisco J.; Romero Sarabia, Alfonso
In this paper, we develop a formula for spacelike surfaces in a 4-
dimensional Lorentzian space form which involves its mean curvature
vector eld and the Gauss curvature of the induced metric and the
Gauss curvature of the second fundamental form associated to a non-
degenerate null normal section. By means of this formula, we stablish
several su cient conditions for compact spacelike surfaces with con-
stant Gauss curvature to have a null umbilical direction. As another
application, we give a new proof of the Liebmann rigidity theorem in
Euclidean, hemispherical and hyperbolic spaces, and in the De Sitter
spacetime.
Some Real Hypersurfaces in Complex and Complex Hyperbolic Quadrics
https://hdl.handle.net/10481/87332
Some Real Hypersurfaces in Complex and Complex Hyperbolic Quadrics
Pérez Jiménez, Juan De Dios
On a real hypersurface in the complex quadric or the complex hyperbolic quadric we can consider the Levi-Civita connection and, for any nonnull real number $k$, the $k$-th generalized Tanaka-Webster connection. We also have a differential operator of first order of Lie type associated to the $k$-th generalized Tanaka-Webster connection. We classify real hypersurfaces in the complex quadric and the complex hyperbolic quadric for which the Lie derivative and the Lie type differential operator coincide when they act on the shape operator of the real hypersurface either in the direction of the structure vector field or in any direction of the maximal holomorphic distribution.
El título del preprint era "Lie derivatives of the shape operator of real hypersurfaces in the complex and complex hyperbolic quadrics" y posteriormente, siguiendo las indicaciones de los reviewers, fue modificado a Some Real Hypersurfaces in Complex and Complex Hyperbolic Quadrics.
Real Hypersurfaces with Killing Shape Operator in the Complex Quadric
https://hdl.handle.net/10481/87329
Real Hypersurfaces with Killing Shape Operator in the Complex Quadric
Pérez Jiménez, Juan De Dios; Jeong, Imsoon; Ko, Junhyung; Suh, Young Jin
We introduce the notion of Killing shape operator for real hypersurfaces in the complex quadric $Q^m = SO_{m+2}/SO_m SO_2$. The Killing shape operator condition implies that the unit normal vector field $N$ becomes $\mathfrak{A}$-principal or $\mathfrak{A}$-isotropic. Then according to each case, we give a complete classification of Hopf real hypersurfaces in $Q^m = SO_{m+2}/SO_m SO_2$ with Killing shape operator.
Ruled Real Hypersurfaces in he Complex Quadric
https://hdl.handle.net/10481/87322
Ruled Real Hypersurfaces in he Complex Quadric
Kimura, Makoto; Lee, Hyunjin; Pérez Jiménez, Juan De Dios; Suh, Young Jin
First we introduce the notions of $\eta$-parallel and $\eta$-commuting shape operator for real hypersurfaces in the complex quadric $Q^m = SO_{m+2}/SO_m SO_2$. Next we give a complete classification of real hypersurfaces in the complex quadric $Q^m$ with such king of shape operators. By virtue of this classification we give a new characterization of ruled real hypersurfaces foliated by complex totally geodesic hyperplanes $Q^{m-1}$ in $Q^m$ whose unit normal vector field in $Q^m$ is $\mathfrak{A}$-principal.