Research
Research
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My research lines are focused on Submanifolds theory, a branch of Differential Geometry where some subsets of differentiable manifolds are studied, on which it is imposed a geometric condition to be able to study them and, at a given moment, to classify them. Common conditions on submanifolds include:
- To have some type of curvature (mean, r-th mean, scalar) constant or bounded.
- To have a distinguished vector field (Killing, conformal, closed conformal, for example).
In the case of the ambient space where the submanifolds are found, I work with space forms, homogeneous spaces, and warped products, although it is also important to know which of these results in the differentiable field extend to more general spaces, such as Alexandrov spaces, Ricci limit spaces and so on.
Needless to say, I regularly collaborate with national and foreign professors and researchers.
Published papers
Complete rotation hypersurfaces with H_k constant in space forms
Palmas
Bulletin of the Brazilian Mathematical Society
1999
O(2)xO(2)-invariant hypersurfaces with zero scalar curvature
Palmas
Archiv der Mathematik
2000
A gap theorem for complete constant scalar curvature in the de Sitter space
Brasil, Colares, Palmas
Journal of Geometry and Physics
2001
Complete spacelike hypersurfaces with constant mean curvature in the De Sitter space: A gap theorem
Brasil, Colares, Palmas
Illinois Journal of Mathematics
2003
Complete hypersurfaces in R^{2n+2} with constant negative 2n-th curvature
Palmas
Archiv der Mathematik
2003
O(m)xO(n) – invariant minimal hypersurfaces in R^{m+n}
Alencar, Barros, Palmas, Reyes, Santos
Annals of Global Analysis and Geometry
2005
Hipersuperficies tipo espacio con curvatura media constante en variedades de Lorentz
Ortega, Palmas
Mathemàtiques
2007
Erratum to A gap theorem for complete constant scalar curvature hypersurfaces in the de Sitter space
Brasil, Colares, Palmas
Journal of Geometry and Physics
2007
On a new class of embedded hypersurfaces in R^{m+n} with nonzero constant mean curvature
Cruz, Palmas, Reyes
Advances in Geometry
2007
Addendum to Complete rotation hypersurfaces with H_k constant in space forms
Colares, Palmas
Bulletin of the Brazilian Mathematical Society
2008
Foliations by (n – 1)-umbilical spacelike hypersurfaces
Colares, Palmas
Matemática Contemporânea
2008
Complete hypersurfaces with constant scalar curvature in spheres
Brasil, Colares, Palmas
Monatshefte für Mathematik
2010
On Riemannian manifolds foliated by (n-1)-umbilical hypersurfaces
Colares, Palmas
Bulletin of the Brazilian Mathematical Society
2011
Shadow boundaries in space forms
Palmas, Ruiz-Hernández
Matemática Contemporânea
2011
Hypersurfaces with a canonical principal direction
Garnica, Palmas, Ruiz-Hernández
Differential Geometry and its Applications
2012
Classification of Constant Angle Hypersurfaces in Warped Products via Eikonal Functions
Garnica, Palmas, Ruiz-Hernández
Boletín de la Sociedad Matemática Mexicana
2012
Spacelike foliations by (n – 1)-umbilical hypersurfaces in spacetimes
Colares, Palmas
The Asian Journal of Mathematics
2013
Spacelike hypersurfaces with a canonical principal direction
Palmas, Ruiz-Hernández
Proceedings of PADGE2012 (Pure and Applied Differential Geometry)
2013
On the geometry of null hypersurfaces in Minkowski space
Navarro, Palmas, Solís
Journal of Geometry and Physics
2014
Minimal translation hypersurfaces in Euclidean space
Munteanu, Palmas, Ruiz-Hernández
Mediterranean Journal of Mathematics
2015
Null hypersurfaces in generalized Robertson-Walker spacetimes
Navarro, Palmas, Solís
Journal of Geometry and Physics
2016
Hypersurfaces with constant higher order mean curvature in space forms
Meléndez, Palmas
Differential Geometry and its Applications
2016
On the total mean curvature of a compact spacelike submanifold in Lorentz-Minkowski spacetime
Palmas, Palomo, Romero
Proceedings of the Royal Society of Edinburgh: Section A – Mathematics
2017
Hypersurfaces with constant scalar curvature in space forms
Alías, Meléndez, Palmas
Differential Geometry and its Applications
2018
Null screen isoparametric hypersurfaces in Lorentzian space forms
Navarro, Palmas, Solís
Mediterranean Journal of Mathematics
2018
Principal configurations around umbilics of spacelike surfaces in null hypersurfaces of R14
Navarro, Palmas, Solís
Differential Geometry and its Applications
2019
Fernández, Palmas, Petean
Discrete and Continuous Dynamical Systems-A
2020
Null screen quasi-conformal hypersurfaces in semi-Riemannian manifolds and applications
Navarro, Palmas, Solís
Mathematische Nachrichten
2020
An ODE reduction method for the semi-Riemannian Yamabe problem on space forms
Fernández, Palmas
Nonlinear Analysis
2021
Null hypersurfaces with screen parallel shape operator
Palmas
Mediterranean Journal of Mathematics
2021
Foliations of doubly warped products by k-umbilical hypersurfaces
Colares, Palmas
Annali di Matematica Pura ed Applicata
2022
Rigidity of hypersurfaces with constant higher order mean curvature in space forms
Meléndez, Palmas
Boletín de la Sociedad Matemática Mexicana
2022
Rotation hypersurfaces in semi-Riemannian space forms of arbitrary index
Garnica, Meléndez, Palmas
Differential Geometry and its Applications
2022
Geometry of null hypersurfaces in Lorentzian space forms
Navarro, Palmas, Solís
Lorentzian Geometry GELOMA 2021 Springer Proceedings
2022
Lorentzian pseudo-parallel surfaces in pseudo-Riemannian space forms
Lobos, Melara, Palmas
Results in Mathematics
2023
On isometric immersions of null manifolds into semi-Riemannian space forms of arbitrary index
Avila, Navarro, Palmas, Solis
International Electronic Journal of Geometry
2023
Equivariant Solutions to the Optimal Partition Problem for the Prescribed Q-Curvature Equation
Fernández, Palmas, Torres Orozco
Journal of Geometric Analysis
2024
Screen isotropic leaves and Simons' formula for null hypersurfaces
Kemajou-Mbiakop, Palmas
Bulletin of the Korean Mathematical Society
2024
Moduli spaces of flat Riemannian metrics on 4-dimensional closed manifolds
García, Palmas
Annali di Matematica Pura ed Applicata
2025
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