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Complete spacelike hypersurfaces on symmetric spacetimes
(IOP Publishing, 2020)
A Lorentz manifold (M, g) is said to be a conformally stationary spacetime if it is endowed with a globally defined conformal timelike vector field K, whereas it is a pp-wave when there is a globally defined parallel ...
A Moser–Bernstein problem for Riemannian warped products
(Springer, 2020)
In this work we deal with an elliptic non-linear problem, which arises naturally from Riemannian geometry. This problem has classically been studied in the the Euclidean n-dimensional space and it is known as the Moser–Bernstein ...
Willmore surfaces and Hopf tori in homogeneous 3-manifolds
(Springer, 2022)
Some 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 E3(κ,τ) with isometry group of dimension ...
Total mean curvature surfaces in the product space S^n x R and applications
(Cambridge University Press, 2023)
The total mean curvature functional for submanifolds into the Riemannian product space S^n × R is considered and its first variational formula is presented. Later on, two second order differential operators are defined and ...
On the symmetries of a Kaehler manifold
(Springer, 2023)
The natural symmetries of Riemannian manifolds are described by the symmetries of its Riemann curvature tensor. In that sense, the most symmetric manifolds are the constant sectional curvature ones. Its natural generalizations ...
Critical points of the solutions to the H_R=H_L surface equation
(Springer, 2023)
Spacelike 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 ...
On complete trapped submanifolds in globally hyperbolic spacetimes
(IOP Publishing, 2023)
The aim of this manuscript is to obtain rigidity and non-existence results for parabolic spacelike submanifolds with causal mean curvature vector field in orthogonally splitted spacetimes, and in particular, in globally ...