A property that characterizes the Enneper surface and helix surfaces
Mediterranean Journal of Mathematics 21, 155 (2024). Electronic ISSN: 1660-5454, Print ISSN: 1660-5446.
Publicaciones
2024
2023
Concircular hypersurfaces and concircular helices in space forms
Mediterranean Journal of Mathematics 20, 320 (2023). Electronic ISSN: 1660-5454, Print ISSN: 1660-5446.
L1-2-type surfaces in 3-dimensional De Sitter and anti De Sitter spaces
Bulletin of the Malaysian Mathematical Sciences Society 46 (2023), Article number: 139. Electronic ISSN: 2180-4206, Print ISSN: 0126-6705.
A generalization of the notion of helix
Turkish Journal of Mathematics 47:4 (2023), 1158-1168. ISSN: 1300-0098.
Concircular helices and concircular surfaces in Euclidean 3-space R3
Hacettepe Journal of Mathematics and Statistics 52:4 (2023), 995-1005. ISSN: 2651-477X.
2019
Slant helices, a new approximation
Turkish Journal of Mathematics 43:1 (2019), 473-485. ISSN: 1300-0098.
2018
Surfaces in S3 of L1-2-type
Bulletin of the Malaysian Mathematical Sciences Society 41:4 (2018), 1759-1771. ISSN: 0126-6705.
2017
Hyperbolic surfaces of L1-2-type
Bulletin of the Iranian Mathematical Society 43:6 (2017), 1769-1779. ISSN: 1735-8515.
Helix surfaces and slant helices in the three-dimensional anti De Sitter space
RACSAM - Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales 111 (2017), 1201-1222. ISSN: 1578-7303.
Slant helices in the three-dimensional sphere
Journal of the Korean Mathematical Society 54 (2017), 1331-1343. ISSN: 0304-9914.
Integrability aspects of the vortex filament equation for pseudo-null curves
International Journal of Geometric Methods in Modern Physics Vol. 14 (2017) 1750090 (21 pages). ISSN: 0219-8878.
2016
Null curve evolution in four-dimensional pseudo-Euclidean space
Advances in Mathematical Physics, Volume 2016 (2016), Article ID 5725234, 15 pages. ISSN: 1687-9120.
Hypersurfaces in S4 that are of Lk-2-type
Bulletin of the Korean Mathematical Society 53:3 (2016), 885-902. ISSN: 1015-8634.
Rectifying curves in the three-dimensional hyperbolic space
Mediterranean Journal of Mathematics 13 (2016), 2199-2214. ISSN: 1660-5446.
Slant helices in the Euclidean 3-space revisited
Bulletin of the Belgian Mathematical Society Simon Stevin 23 (2016), 133-150. ISSN: 1370-1444.
2015
Lk-2-type hypersurfaces in hyperbolic spaces
Taiwanese Journal of Mathematics 19, No. 1 (2015), 221-242. ISSN: 1027-5487.
A Lie algebra structure on variation vector fields along curves in 2-dimensional space forms
Journal of Geometry and Physics 88 (2015), 94-104. ISSN: 0393-0440.
Rectifying curves in the three-dimensional sphere
Journal of Mathematical Analysis & Applications 421 (2015), 1855-1868. ISSN: 0022-247X.
2014
Hamiltonian structure for null curve evolution
Nonlinearity 27 (2014), 2627-2641. ISSN: 0951-7715.
2013
A variational characterization and geometric integration for Bertrand curves
Journal of Mathematical Physics 54 (2013) 043508, 12 pág. ISSN: 0022-2488.
Bertrand curves in non-flat three-dimensional (Riemannian or Lorentzian) space forms
Bulletin of the Korean Mathematical Society 50:4 (2013), 1109-1126. ISSN: 1015-8634.
Hypersurfaces in pseudo-Euclidean spaces satisfying a linear condition on the linearized operator of a higher order mean curvature
Differential Geometry and its Applications 31 (2013), 175-189. ISSN: 0926-2245.
Hypersurfaces in non-flat pseudo-Riemannian space forms satisfying a linear condition in the linearized operator of a higher order mean curvature
Taiwanese Journal of Mathematics 17 (2013), 15-45. ISSN: 1027-5487.
2012
Bertrand curves in the three-dimensional sphere
Journal of Geometry and Physics 62 (2012), 1903-1914. ISSN: 0393-0440.
Hypersurfaces in non-flat Lorentzian space forms satisfying LkΨ=AΨ+b
Taiwanese Journal of Mathematics 16 (2012), 1173-1203. ISSN: 1027-5487.
2011
Hypersurfaces in the Lorentz-Minkowski space satisfying LkΨ=AΨ+b
Geometriae Dedicata 153 (2011), 151-175. ISSN: 0046-5755.
2007
Relativistic particles and the geometry of 4-D null curves
Journal of Geometry and Physics 57 (2007), 2124-2135. ISSN: 0393-0440.
2006
Particles with curvature and torsion in three-dimensional pseudo-Riemannian space forms
Journal of Geometry and Physics 56 (2006), 1666-1687. ISSN: 0393-0440.
2005
Relativistic particles with rigidity and torsion in D=3 spacetimes
Classical and Quantum Gravity 22 (2005), 489-513.
2004
Relativistic particles with rigidity along light-like curves
En Horizons In World Physics, Volume 245, Tori V. Lynch (Editor), editado por Nova Science Publishers Inc., 2004, ISBN:1-59454-063-2.
Geometry of relativistic particles with torsion
International Journal of Modern Physics A 11 (2004), 1737-1745.
2003
s-degenerate curves in Lorentzian space forms
Journal of Geometry and Physics 45 (2003), 116-129.
Geometry of lightlike submanifolds in Lorentzian space forms
Publicaciones de la RSME vol. 5 (2003), 125-139.
El libro de LaTeX
Prentice Hall, Pearson Educación, Madrid, 2003. ISBN: 84-205-3779-9.
2002
Null generalized helices in Lorentz-Minkowski spaces
Journal of Physics A: Mathematics and General 35 No. 39 (2002) 8243-8251.
Geometrical particle models on 3D null curves
Physics Letters B 543 (2002), 311-317.
Null helices and degenerate curves in Lorentzian spaces
Proceedings of the International Conference Differential Geometry, Valencia 2001, eds. Vicente Miquel y Olga Gil, 2002, ISBN 981-02-4906-3.
Degenerate curves in pseudo-Euclidean spaces of index two
Proceedings of the Third International Conference on Geometry, Integrability and Quantization III, eds. I.M. Mladenov y G.L. Naber, 2002, ISBN 954-90618-3-3.
2001
Null helices in Lorentzian space forms
International Journal of Modern Physics A 16 (2001), 4845-4863.
Geometric integration of the Betchov-Da Rios equation in a Gravity-Electromagnetism unified model
Journal of Geometry and Physics 40 (2001), 1-12.
General helices in the 3-dimensional Lorentzian space forms
Rocky Mountain Journal of Mathematics 31 (2001), 373-388.
Characterization of null curves in Lorentz-Minkowski spaces
Publicaciones de la RSME, vol. 3 (2001), 221-226.
2000
On the Gauss map of B-scrolls in 3-dimensional Lorentzian space forms
Chechoslovak Mathematical Journal 50 (2000), 699-704.
A criterion to reduce variables into the Willmore-Chen variational problem and some applications
Transactions of the American Mathematical Society 352 (2000), 3015-3027.
Conformal tension in string theories and M-theory
Nuclear Physics B 584 (2000), 719-748.
LaTeX, una imprenta en sus manos
ADI, Madrid, 2000. ISBN: 84-920381-9-5, DL: M-1.728-2000.
1999
Lawson-type problems in non standard 3-spheres
The Quarterly Journal of Mathematics 50 (1999), 385-388.
Solutions of the Betchov-Da Rios soliton equation: A Lorentzian approach
Journal of Geometry and Physics 31 (1999), 217-228.
Solutions of the Betchov-Da Rios soliton equation in the anti-De Sitter 3-space
New Approaches in Nonlinear Analysis, Ed. Th.M. Rassias, Hadronic Press, Inc., Palm Harbor, Florida, 1999, pp. 51-71, ISBN: 1-57485-042-3/pbk.
1998
On the Gauss map of B-scrolls
Tsukuba Journal of Mathematics 22 (1998), 371-377.
Biharmonic Hopf cylinders
Rocky Mountain Journal of Mathematics 28 (1998), 957-975.
Willmore tori and Willmore-Chen submanifolds in pseudo-Riemannian spaces
Journal of Geometry and Physics 28 (1998), 45-66.
A new viewpoint on geometry of a lightlike hypersurface in a semi-Euclidean space
Saitama Journal of Mathematics 16 (1998), 31-38.
1997
Pseudo-spherical and pseudo-hyperbolic submanifolds via the quadric representation, I
Archiv der Mathematik 68 (1997), 520-528.
Pseudo-spherical and pseudo-hyperbolic submanifolds via the quadric representation, II
Archiv der Mathematik 69 (1997), 82-88.
1996
A quadric representation of pseudo-Riemannian products immersions
Tsukuba Journal of Mathematics 20 (1996), 1-22.
Biharmonic products in the normal bundle
Commentarii Mathematici Universitatis Sancti Pauli 45 (1996), 147-158.
Semi-Riemannian constant mean curvature surfaces via its quadric representation
Houston Journal of Mathematics 22 (1996), 533-546.
1995
Hypersurfaces in space forms satisfying the condition Δx=Ax+B
Transactions of the American Mathematical Society 347 (1995), 1793-1801.
Hypersurfaces in the non-flat Lorentzian space forms with a characteristic eigenvector field
Journal of Geometry 52 (1995), 10-24.
Hopf cylinders, B-scrolls and solitons of the Betchov-Da Rios equation in the 3-dimensional anti-De Sitter space
Comptes Rendus de l'Académie des Sciences Paris 321 (1995), 505-509.
Classification of certain semi-Riemannian constant mean curvature surfaces
Geometry and Topology of Submanifolds vol. VII, 132-135, 1995, World Scientific Publ. Co.
1994
2-type surfaces in S13 and H13
Tokyo Journal of Mathematics 17 (1994), 447-454.
1993
Surfaces in Lorentzian space forms satisfying the condition Δx=Ax+B
Geometry and Topology of Submanifolds vol. VI, pp. 3-15, 1993, World Scientific Publ. Co.
1992
Surfaces in the 3-dimensional Lorentz-Minkowski space satisfying Δx=Ax+B
Pacific Journal of Mathematics 156 (1992), 201-208.
Classifying pseudo-Riemannian hypersurfaces by means of certain characteristic differential equations
The problem of Plateau: A tribute to Jesse Douglas and Tibor Radó. Edited by Th. M. Rassias, pp. 53-75, 1992, World Scientific Publ. Co.
Submanifolds in pseudo-Euclidean spaces satisfying the condition Δx=Ax+B
Geometriae Dedicata 42 (1992), 345-354.
Null 2-type hypersurfaces in a Lorentz space
Canadian Mathematical Bulletin 35 (1992), 354-360.
Classifying hypersurfaces in the Lorentz-Minkowski space with a characteristic eigenvector
Tokyo Journal of Mathematics 15 (1992), 451-459.
On surfaces in the 3-dimensional Lorentz-Minkowski space
Pacific Journal of Mathematics 152 (1992), 93-110.
Finite type surfaces of revolution
Rivista di Matematica Pura et Applicata 12 (1992), 75-87.
1991
Finite type ruled manifolds shaped on spherical submanifolds
Archiv der Mathematik 57 (1991), 97-104.
On a certain class of conformally flat Euclidean hypersurfaces
Lecture Notes in Mathematics n. 1481, (1991), 48-54.
Null finite type hypersurfaces in space forms
Kodai Mathematical Journal 14 (1991), 406-419.
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Ultima actualización: 11/07/2024