A5018768944- Geometric Analysis and Curvature Flows
- Advanced Differential Geometry Research
- Geometry and complex manifolds
- Advanced Mathematical Modeling in Engineering
- Point processes and geometric inequalities
- Nonlinear Partial Differential Equations
- Mathematics and Applications
- Geometric and Algebraic Topology
- Advanced Numerical Analysis Techniques
- Algebraic and Geometric Analysis
- Differential Equations and Numerical Methods
- Differential Equations and Boundary Problems
- Numerical methods in inverse problems
- Advanced Theoretical and Applied Studies in Material Sciences and Geometry
- Analytic and geometric function theory
- Computational Geometry and Mesh Generation
- Elasticity and Material Modeling
- 3D Shape Modeling and Analysis
- Mathematical Dynamics and Fractals
- Social Sciences and Policies
- Relativity and Gravitational Theory
- Experimental and Theoretical Physics Studies
- Educational Technology in Learning
- Mexican Socioeconomic and Environmental Dynamics
- Advanced Differential Equations and Dynamical Systems
Universidad de Granada
2016-2025
Hospital Virgen del Puerto
2001-2024
Robotnik (Spain)
2022
Ankara University
2022
Fırat University
2021
American University of Sharjah
2019
Alexandru Ioan Cuza University
2012-2015
We review part of the classical theory curves and surfaces in 3-dimensional Lorentz-Minkowski space.We focus spacelike with constant mean curvature pointing differences similarities Euclidean space.Contents 1.The space E 3 1 45 2. Curves Minkowski 53 3. Surfaces 72 4. Spacelike 91 5. Elliptic equations on cmc 99 References 106
We consider a curve <TEX>$\alpha$</TEX>= <TEX>$\alpha$</TEX>(s) in Minkowski 3-space <TEX>$E_1^3$</TEX> and denote by {T, N, B} the Frenet frame of <TEX>$\alpha$</TEX>. say that <TEX>$\alpha$</TEX> is slant helix if there exists fixed direction U such function <N(s)U> constant. In this work we give characterizations helices terms curvature torsion Finally, discuss tangent binormal indicatrices curves, proving they are <TEX>$E_1^3$</TEX>.
A constant angle surface in Minkowski space is a spacelike whose unit normal vector field makes hyperbolic with fixed timelike vector. In this work we study and classify these surfaces. particular, show that they are flat. Next prove tangent developable (resp. cylinder, cone) if only the generating curve helix straight line, circle).
We classify the family of spacelike maximal surfaces in Lorentz-Minkowski 3-space L 3 which are foliated by pieces circles. This space contains a curve singly periodic R that play same role as Riemann’s minimal examples E. As consequence, we prove annuli bounded two circles parallel planes either catenoid or surface R.
In the homogeneous space Sol3, a translation surface is parametrized by x(s,t) = α(s) ∗ β(t), where α and β are curves contained in coordinate planes denotes group operation of Sol3. this paper we study surfaces Sol3 whose mean curvature vanishes.
We study surfaces in Euclidean space which are obtained as the sum of two curves or that graphs product functions. consider problem finding all these with constant Gauss curvature. extend results to non-degenerate Lorentz-Minkowski space.
Of all public assets, road infrastructure tops the list. Roads are crucial for economic development and growth, providing access to education, health, employment. The maintenance, repair, upgrade of roads therefore vital users' health safety as well a well-functioning prosperous modern economy. EU-funded HERON project will develop an integrated automated system adequately maintain infrastructure. In turn, this reduce accidents, lower maintenance costs, increase network capacity efficiency....
Abstract We classify all rotational surfaces in Euclidean space whose principal curvatures κ 1 and 2 satisfy the linear relation , where a b are two constants. As consequence of this classification, we find closed (embedded not embedded) periodic with geometric behaviour similar to Delaunay surfaces. Finally, give variational characterization generating curves these
Abstract The concept of catenary has been recently extended to the sphere and hyperbolic plane by second author (López, arXiv:2208.13694 ). In this work, we define catenaries on any Riemannian surface. A a surface is critical point potential functional, where calculate with intrinsic distance fixed reference geodesic. Adopting semi-geodesic coordinates around geodesic, characterize using their curvature. Finally, after revisiting space-form catenaries, consider surfaces revolution (where...
Smooth axially symmetric Helfrich topological spheres are either round or else they must satisfy a second order equation known as the reduced membrane [17]. In this paper, we show that, conversely, closed genus zero solutions of which, in addition, rescaling condition spheres. We also exploit characterization to geometrically describe these surfaces and present convincing evidence that with respect suitable plane orthogonal axis rotation belong particular infinite discrete family surfaces.
Spacelike intrinsic rotational surfaces with constant mean curvature in the Lorentz-Minkowski space $\E_1^3$ have been recently investigated by Brander et al., extending known Smyth's Euclidean space. In this paper, we give an approach to analogue of . Assuming that surface is coordinates $(u,v)$ and conformal factor $\rho(u)^2$, replace constancy property Weingarten endomorphism $A$ can be expressed as $\Phi_{-\alpha(v)}\left(\begin{array}{ll}\lambda_1(u)&0\\...
In this paper, we study surfaces in Euclidean 3-space that satisfy a Weingarten condition of linear type as κ 1 = mκ 2 + n, where m and n are real numbers denote the principal curvatures at each point surface. We investigate existence such parametrized by uniparametric family circles. prove only exist revolution classical examples minimal discovered Riemann. The latter situation occurs case (m, n) (-1, 0).
In this paper we define and classify all surfaces in the three-dimensional Lie group Sol3 whose normals make constant angle with a left-invariant vector field.