Constant angle surfaces in 4-dimensional Minkowski space
Por:
Bayard, Pierre, Monterde, Juan, Volpe, Raul C.
Publicada:
1 ene 2019
Resumen:
We first define a complex angle between two oriented spacelike planes in 4-dimensional Minkowski space, and then study the constant angle surfaces in that space, i.e. the oriented spacelike surfaces whose tangent planes form a constant complex angle with respect to a fixed spacelike plane. This notion is the natural Lorentzian analogue of the notion of constant angle surfaces in 4-dimensional Euclidean space. We prove that these surfaces have vanishing Gauss and normal curvatures, obtain representation formulas for the constant angle surfaces with regular Gauss maps and construct constant angle surfaces using PDE's methods. We then describe their invariants of second order and show that a surface with regular Gauss map and constant angle ??0[p/2] is never complete. We finally study the special cases of surfaces with constant angle p/2[p], with real or pure imaginary constant angle and describe the constant angle surfaces in hyperspheres and lightcones. © 2019
Filiaciones:
Bayard, Pierre:
Facultad de Ciencias, Universidad Nacional Autónoma de México, Av. Universidad 3000, Circuito Exterior S/N, Delegación Coyoacán, Ciudad Universitaria, CDMX C.P. 04510, Mexico
Univ Nacl Autonoma Mexico, Fac Ciencias, Av Univ 3000,Circuito Exterior S-N,Ciudad Univ, Cdmx 04510, Mexico
Monterde, Juan:
Facultad de Matemáticas, Universidad de Valencia, Dr. Moliner, 50, 46100 Burjassot (Valencia), España, Spain
Univ Valencia, Fac Matemat, Dr Moliner 50, E-46100 Burjassot, Valencia, Spain
Volpe, Raul C.:
Facultad de Matemáticas, Universidad de Valencia, Dr. Moliner, 50, 46100 Burjassot (Valencia), España, Spain
Univ Valencia, Fac Matemat, Dr Moliner 50, E-46100 Burjassot, Valencia, Spain
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