1,720,976 research outputs found
New examples of entire maximal graphs in H2×R1
No full textAbstractIn this paper we obtain new explicit examples of complete and non-complete entire maximal graphs in H2×R1. The existence of these entire maximal graphs shows that entire maximal graphs in this Lorentzian product space are not necessarily complete, on the contrary that in the Lorentz–Minkowski space. Moreover, in [A.L. Albujer, L.J. Alías, Calabi–Bernstein results for maximal surfaces in Lorentzian product spaces, Preprint, 2006], the author jointly with Alías gave a Calabi–Bernstein theorem for maximal surfaces immersed into the Lorentzian product space M2×R1, where M2 is a connected Riemannian surface of non-negative Gaussian curvature, and these examples show that the assumption on KM is necessary
New examples of entire maximal graphs in H2×R1
No full textIn this paper we obtain new explicit examples of complete and non-complete entire maximal graphs in H2 × R1. The existence of these entire maximal graphs shows that entire maximal graphs in this Lorentzian product space are not necessarily complete, on the contrary that in the Lorentz–Minkowski space. Moreover, in [A.L. Albujer, L.J. Alías, Calabi–Bernstein results for maximal surfaces in Lorentzian product spaces, Preprint, 2006], the author jointly with Alías gave a Calabi–Bernstein theorem for maximal surfaces immersed into the Lorentzian product space M2 × R1, where M2 is a connected Riemannian surface of non-negative Gaussian curvature, and these examples show that the assumption on KM is necessary.FPU Grant AP2004-4087 from Secretaría de Estado de Universidades e Investigación, MEC, and MEC/FEDER project MTM2004-04934-C04-02, Spain
A geometrical interpretation of the null sectional curvature
No full textA geometrical interpretation is given for the null sectional curvature of degenerate planes in a Lorentzian manifold. This interpretation is based on a generalization to the indefinite case of the squaroids of Levi-Civita. Further, it is shown that a three-dimensional, conformally flat Lorentzian manifold has isotropic and spatially constant null sectional curvature if and only if it is locally a Robertson–Walker manifold.The first author was partially supported by MEC project MTM2007-64504, and Fundación Séneca project 04540/GERM/06, Spain. The second author was partially supported by the Spanish MEC Grant MTM2007-60731 with FEDER funds and the Junta de Andalucía Regional Grant P06-FQM-01951. This research is a result of the activity developed within the framework of the Programme in Support of Excellence Groups of the Región de Murcia, Spain, by Fundación Séneca, Regional Agency for Science and Technology (Regional Plan for Science and Technology 2007–2010)
Geometric properties of surfaces with the same mean curvature in R^3 and L^3
Get PDFSpacelike surfaces in the Lorentz–Minkowski space L^3 can be endowed with two different Riemannian metrics, the metric inherited from L^3 and the one induced by the Euclidean metric of R^3. It is well known that the only surfaces with zero mean curvature with respect to both metrics are open pieces of the helicoid and of
spacelike planes. We consider the general case of spacelike surfaces with the same mean curvature with respect to both metrics. One of our main results states that those surfaces have non-positive Gaussian curvature in R^3. As an application of this result, jointly with a general argument on the existence of elliptic points, we present several geometric consequences for the surfaces we are considering. Finally, as any spacelike surface in L3 is locally a graph, our surfaces are locally determined by the solutions to the H_R = H_L surface equation. Some uniqueness results for the Dirichlet problem associated to this equation are given.The first author is partially supported by MINECO/FEDER project reference MTM2015-65430-P, Spain, and Fundación Séneca project reference 19901/GERM/15, Spain. Her work is a result of the activity developed within the framework of the Program in Support of Excellence Groups of the Región de Murcia, Spain, by Fundación Séneca, Science and Technology Agency of the Región de Murcia. The second author is partially supported by the Spanish Ministry of Economy and Competitiveness and European Regional Development Fund (ERDF), project MTM2013-47828-C2-1-P
Willmore surfaces and Hopf tori in homogeneous 3-manifolds
No full textSome classification results for closed surfaces in Berger spheres are presented. On the one hand, a Willmore functional for isometrically immersed surfaces into an homogeneous space E^3(k, t) with isometry group of dimension 4 is defined and its first variational formula is computed. Then, we characterize Clifford and Hopf tori as the only Willmore surfaces satisfying a sharp Simons-type integral inequality. On the other hand, we also obtain some integral inequalities for closed surfaces with constant extrinsic curvature in E^3(k, t), becoming equalities if and only if the surface is a Hopf torus in a Berger sphere.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The authors would like to heartily thank the referee for his/her valuable remarks and comments. The first author is partially supported by MICINN/FEDER Project PGC2018-097046-B-I00, by the Regional Government of Andalusia ERDEF Project PY20-01391 and Fundación Séneca Project 19901/GERM/15, Spain. Her work is a result of the activity developed within the framework of the Program in Support of Excellence Groups of the Región de Murcia, Spain, by Fundación Séneca, Science and Technology Agency of the Región de Murcia. The second author is also partially supported by CNPq, Brazil, under the Grant 431976/2018-0
Non-degenerate Anisocurved Surfaces in Homogeneous 3-Manifolds
Get PDFIn this manuscript we consider non-degenerate surfaces Σ2 immersed in a 3-dimensional homogeneous space L3(κ, τ ) endowed with two different metrics, the one induced by the Riemannian metric of E3(κ, τ ) and the non-degenerate metric inherited by the Lorentzian one of L3(κ, τ ). Therefore, we have two different geometries on Σ2 and we can compare them. In particular, we can consider the Gaussian curvature functions which respect to both metrics and study the geometry of the surfaces satisfying that both Gaussian curvature functions are opposite. We will call these surfaces anisocurved surfaces. In order to obtain our main results we also need to impose some extra assumptions regarding the extrinsic curvatures with respect to both metrics.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The first author is partially supported by the Spanish MICINN project PID2021-126217NB-I00. The second author is also partially supported by CNPq, Brazil, under the grant 311124/2021-6 and Propesqi (UFPE)
Spacelike hypersurfaces with constant mean curvature in the steady state space
Get PDFWe consider complete spacelike hypersurfaces with constant mean curvature in the open region of de Sitter space known as the steady state space. We prove that if the hypersurface is bounded away from the infinity of the ambient space, then the mean curvature must be H = 1. Moreover, in the 2-dimensional case we obtain that the only complete spacelike surfaces with constant mean curvature which are bounded away from the infinity are the totally umbilical flat surfaces. We also derive some other consequences for hypersurfaces which are bounded away from the future infinity. Finally, using an isometrically equivalent model for the steady state space, we extend our results to a wider family of spacetimes.The first author was supported by FPU Grant AP2004-4087 from Secretaría de Estado de Universidades e Investigación, MEC Spain. This research was partially supported by MEC project MTM2007-64504 and Fundación Séneca project 04540/GERM/06, Spain
Critical points of the solutions to the H_R=H_L surface equation
No full textSpacelike surfaces with the same mean curvature in R^3 and L^3 are locally described as the graph of the solutions to the H_R = H_L surface equation, which is an elliptic partial differential equation except at the points at which the gradient vanishes, because the equation degenerates. In this paper we study precisely the critical points of the solutions to such equation. Specifically, we give a necessary geometrical condition for a point to be critical, we obtain a new uniqueness result for the Dirichlet problem related to the H_R = H_L surface equation and we get a Heinz-type bound for the inradius of the domain of any solution to such equation, improving a previous result by the authors. Finally, we also get a bound for the inradius of the domain of any function of class C^2 in terms of the curvature of its level curves.Funding for open access publishing: Universidad de Córdoba/CBUA
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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