# Miguel OrtegaUniversity of Granada | UGR · Department of Geometry and Topology

Miguel Ortega

Mathematics

## About

49

Publications

3,467

Reads

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303

Citations

Citations since 2016

Introduction

Right now, I study Semiriemannian Geometry, both local and global, including the Riemannian and Lorentzian cases.

Additional affiliations

October 1999 - present

## Publications

Publications (49)

We generalise the notion of translating solitons in Generalised Robertson-Walker sapcetimes, which come equipped with a natural conformal Killing time-like vector field. We single out three one-parameter families of warping functions for which these objects exist, and we fully classify the corresponding Grim Reapers -- translation-invariant soliton...

The main two families of real hypersurfaces in complex space forms are Hopf and ruled. However, very little is known about real hypersurfaces in the indefinite complex projective space CPpn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \use...

We study new examples of translating solitons of the mean curvature flow, especially in Minkowski space. We consider for this purpose manifolds admitting submersions and cohomegeneity one actions by isometries on suitable open subsets. This general setting also covers the classical Euclidean examples. As an application, we completely classify time-...

It is very well known that Hopf real hypersurfaces in the complex projective space can be locally characterized as tubes over complex submanifolds. This also holds true for some, but not all, Hopf real hypersurfaces in the complex hyperbolic space. The main goal of this paper is to show, in a unified way, how to construct Hopf real hypersurfaces in...

The main two families of real hypersurfaces in complex space forms are Hopf and ruled. However, very little is known about real hy- persurfaces in the indeﬁnite complex projective space CP n p . In a previous work, Kimura and the second author introduced Hopf real hypersurfaces in CP n p . In this paper, ruled real hypersurfaces in the indeﬁnite co...

We study new examples of translating solitons of the mean curvature flow, especially in Minkowski space. We consider for this purpose manifolds admitting submersions and cohomegeneity one actions by isometries on suitable open subsets. This general setting also covers the classical Euclidean examples. As an application, we completely classify timel...

We deal with solitons of the mean curvature flow. The definition of \textit{translating solitons on a lightlike direction} in Minkowski 3-space is introduced. Firstly, we classify those which are graphical, \textit{translation surfaces}, obtaining spacelike and timelike, entire and not entire, complete and incomplete examples. Among them, all our t...

The space of invariant affine connections on every 3-Sasakian homogeneous
manifold of dimension at least 7 is described. In particular, the remarkable subspaces of
invariant affine metric connections, and the subclass with skew-torsion, are also determined.
To this aim, an explicit construction of all 3-Sasakian homogeneous manifolds is exhibited....

The space of invariant affine connections on every 3-Sasakian homogeneous manifold of dimension at least seven is described. In particular, the subspace of invariant affine metric connections and the subclass with skew torsion are also determined. To this aim, an explicit construction of all 3-Sasakian homogeneous manifolds is exhibited. It is show...

We wish to attack the problems that H.~Anciaux and K.~Panagiotidou posed in [1], for non-degenerate real hypersurfaces in indefinite complex projective space. We will slightly change these authors' point of view, obtaining cleaner equations for the almost contact metric structure. To make the theory meaningful, we construct new families of non-dege...

In this paper, we recall some general properties and theorems about Translating Solitons in Semi Riemannian Manifolds. Moreover, we investigate those which are invariant by the action of a Lie group of isometries of the ambient space, by paying attention to the behaviour close to the singular orbit (if any) and at infinity. Then, we provide some re...

In this paper, we recall some general properties and theorems about Translating Solitons in Semi Riemannian Manifolds. Moreover, we investigate those which are invariant by the action of a Lie group of isometries of the ambient space, by paying attention to the behaviour close to the singular orbit (if any) and at infinity. Then, we provide some re...

In this paper, we introduce a notion of (vertical) translating solitons in a product of a semi- Riemannian manifold (M,g) with the real line. Mainly, we restrict our attention to those which are the graph of a smooth function u. When dealing with submersions, we show a criteria to lift (or project) translating solitons from the base manifold to the...

We classify Riemannian surfaces admitting associated families in three
dimensional homogeneous spaces with four-dimensional isometry groups and in a
wide family of (semi- Riemannian) warped products, with an extra natural
condition. We prove that, provided the surface is not totally umbilical, such
families exist in both cases if and only if the am...

We give necessary and sufficient conditions for a semi-Riemannian manifold of
arbitrary signature to be locally isometrically immersed into certain warped
products. Then, we describe a way to use the structure equations of such
immersions to construct foliations of marginally trapped surfaces in a
four-dimensional Lorentzian spacetimes. We point ou...

On a Riemannian almost product manifold, the notion of a componentwise conformal vector field is introduced and several examples are exhibited. We show that this class of vector fields is a conformal invariant. For a compact manifold, a Bochner type integral formula for the Ricci tensor on such vector fields is obtained. Then, integral inequalities...

The model of massless relativistic particle relying in a curvature-dependent action functional is considered in the framework of generalized Robertson–Walker 4-spacetimes. The discussion is based on the number of nonvanishing Frenet curvatures, and we obtain characterizations, examples, and nonexistence results for the critical points of the action...

Hyperbolic metrics on Riemann surfaces and spacelike CMC-1 surfaces in de Sitter 3-space, Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara and Kotaro Yamada. - Bernstein results and parabolicity of maximal surfaces in Lorentzian product spaces, Alma L. Albujer and Luis J. Alias, Calabi. - Umbilical-Type Surfaces in Sp...

By using the classical Hopf map, we construct another fibration that allows us to obtain examples of marginally trapped tori and marginally outer trapped tubes (MOTT) which are foliated by tori, all of them embedded in a closed Friedman-Lemaître-Robertson-Walker 4-spacetime. In addition, we show examples of MOTTs with any causal character.

The notion of orthogonally conformal vector field on a Riemannian
manifold is introduced. This class of vector fields properly
includes the normalization of nowhere zero conformal ones. It is
clarified in several examples. An integral inequality which
relates the existence of orthogonally conformal vector fields with
properties of the Ricci tensor...

In the present paper we provide new examples of marginally trapped surfaces
and tubes in FLRW spacetimes by using a basic relation between these objects
and CMC surfaces in 3-manifolds. We also provide a new method to construct
marginally trapped surfaces in closed FLRW spacetimes, which is based on the
classical Hopf map. The utility of this metho...

The Gauss map of non-degenerate surfaces in the three-dimensional Minkowski space are viewed as dynamical fields of the two-dimensional O(2, 1) Nonlinear Sigma Model. In this setting, the moduli space of solutions with rotational symmetry is completely determined. Essentially, the solutions are warped products of orbits of the 1-dimensional groups...

A spacelike surface in a Lorentzian manifold whose mean curvature vector is lightlike everywhere is called marginally trapped. The classification of marginally trapped surfaces in Minkowski 4-space which are invariant under a subgroup of the Lorentz group that leaves invariant a lightlike direction, i.e. the so-called screw invariant surfaces, is o...

A local classification of spacelike surfaces in Minkowski 4-space, which are invariant under spacelike rotations, and with mean curvature vector either vanishing or lightlike, is obtained. Furthermore, the existence of such surfaces with prescribed Gaussian curvature is shown. A procedure is presented to glue several of these surfaces with intermed...

The extremal and partly marginally trapped surfaces in the Minkowski 4-space, which are invariant under the group of boost isometries, are classified. Moreover, it is shown that there do not exist extremal surfaces of this kind with constant Gaussian curvature. A procedure is given in order to construct a partly marginally trapped surface by gluing...

The model of a massless relativistic particle with curvature-dependent Lagrangian is well known in (d+1)-dimensional Minkowski space. For other gravitational fields less rigid than those with constant (zero) curvature only a few results are known. In this paper, we give a geometric approach in order to solve the field equations associated with that...

We obtain the complete space of solutions, in the two-dimensional O(3) nonlinear sigma model, which are foliated by Villarceau circles. In particular, we prove the existence of solitons that admit a foliation by nonparallel circles. This contrasts with the Plateau context, where solitons foliated by nonparallel circles cannot exist. These solitons...

We prove the nonexistence of real hypersurfaces in nonflat complex space forms whose Jacobi operator associated to the structure vector field is parallel. In order to prove this result we also obtain the nonexistence of several classes of non homogeneous real hypersurfaces in complex projective space.

The model governed by an action measuring the total proper acceleration of trajectories provides a nice framework one to describe the dynamics of massless relativistic particles. In high rigidity cases, metrics with constant curvature, the model is consistent only in spherical three spaces and in three-dimensional anti de Sitter backgrounds, accord...

. Congruent classes of Frenet curves of order 2 in the complex quadric are studied, obtaining that each congruence class is
a level set of a family of certain smooth functions, that are generalizations of isoparametric functions on the unit sphere
in the tangent space of the complex quadric.

Pseudo-parallel real hypersurfaces in complex space forms can be defined as an extrinsic analogues of pseudo-symmetric real hypersurfaces, that generalize the notion of semi-symmetric real hypersurface. In this paper a classification of the pseudo-parallel real hypersurfaces in a non-flat complex space forms is obtained.

From the classical differential equation of Jacobi fields, one naturally defines the Jacobi operator of a Riemannian manifold with respect to any tangent vector. A straightforward computation shows that any real, complex and quaternionic space forms satisfy that any two Jacobi operators commute. In this way, we classify the real hypersurfaces in qu...

It has been proved there axe no semi-parallel real hypersurfaces in the complex projective space ℂPn, n ≥ 3, and in any non-flat complex space form of complex dimension 2. Also, characterizations of geodesic hyperspheres and ruled real hypersurfaces in ℂPn, n ≥ 3, have been obtained by considering some other curvature conditions. We generalize thes...

A Riemannian manifold satisfies the axiom of 2-planes if at each point, there are suficiently many totally geodesic surfaces passing through that point. Real hypersurfaces in quaternionic space forms admit nice families of tangent planes, namely, totally real, half-quaternionic and quaternionic. Several definitions of axiom of planes arise naturall...

We study real hypersurfaces with constant quaternionic sectional curvature in the quaternionic hyperbolic space and the action of the curvature operator on the Weingarten endomorphism. We also introduce examples of ruled real hypersurfaces.

A Riemannian manifold M satisfies the axiom of 2-planes if at each point
$ p\in{M} $
and each tangent 2-plane V at the point, there exists a totally geodesic submanifold L with
$ p\in{L} $
and
$ T_pL=V $
. On the other hand, real hypersurfaces in complex space forms have nice families of tangent 2-planes. If we restrict the above definition t...

We classifyD-Einstein real hypersurfaces of quaternionic space forms, obtaining as a consequence the non-existence of Ricci-parallel real
hypersurfaces in the quaternionic hyperbolic space.

In this paper we classify real hypersurfaces with constant totally real bisectional curvature in a non flat complex space
form M
m
(c), c ≠ 0 as those which have constant holomorphic sectional curvature given in [6] and [13] or constant totally real sectional
curvature given in [11].

We prove the non-existence of Einstein real hypersurfaces of quaternionic hyperbolic space.

## Questions

Question (1)

$M/G$ is the usual quotient, or rather, the space of orbits.