General rotational surfaces in the 4-dimensional Minkowski space

General rotational surfaces as a source of examples of surfaces in the 4-dimensional Euclidean space were introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the basis of our invariant theory of spacelike surfaces we study general rotational surfaces with special invariants. We describe analytically the flat general rotational surfaces and the general rotational surfaces with flat normal connection. We classify completely the minimal general rotational surfaces and the general rotational surfaces consisting of parabolic points.

General rotational surfaces in the 4-dimensional Minkowski space

General rotational surfaces as a source of examples of surfaces in the 4-dimensional Euclidean space were introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the basis of our invariant theory of spacelike surfaces we study general rotational surfaces with special invariants. We describe analytically the flat general rotational surfaces and the general rotational surfaces with flat normal connection. We classify completely the minimal general rotational surfaces and the general rotational surfaces consisting of parabolic points.

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  • Chen BY. Geometry of Submanifolds. New York, NY, USA: Marcel Dekker, 1973.
  • Ganchev G, Milousheva V. On the theory of surfaces in the four-dimensional Euclidean space. Kodai Math J 2008; 31: 183–198.
  • Ganchev G, Milousheva, V. Invariants and Bonnet-type theorem for surfaces inR4. Cent Eur J Math 2010; 8: 993–1008.
  • Ganchev G, Milousheva V. Invariants of lines on surfaces inR4. C R Acad Bulgare Sci 2010; 63: 835–842.
  • Ganchev G, Milousheva V. Chen rotational surfaces of hyperbolic or elliptic type in the four-dimensional Minkowski space. C R Acad Bulgare Sci 2011; 64: 641–652.
  • Ganchev G, Milousheva V. An invariant theory of spacelike surfaces in the four-dimensional Minkowski space. Mediterr J Math 2012; 9: 267–294.
  • Gheysens L, Verheyen P, Verstraelen L. Sur les surfacesA ou les surfaces de Chen. C R Acad Sci Paris 1981; 292: 913–916 (in French).
  • Gheysens L, Verheyen P, Verstraelen L. Characterization and examples of Chen submanifolds. J Geom 1983; 20: 47–
  • Haesen S, Ortega M. Boost invariant marginally trapped surfaces in Minkowski 4-space. Classical Quant Grav 2007; 24: 5441–5452.
  • Haesen S, Ortega M. Marginally trapped surfaces in Minkowski 4-space invariant under a rotational subgroup of the Lorentz group. Gen Relat Gravit 2009; 41: 1819–1834.
  • Liu H, Liu G. Hyperbolic rotation surfaces of constant mean curvature in 3-de Sitter space. Bull Belg Math Soc Simon Stevin 2000; 7: 455–466.
  • Liu H, Liu G. Weingarten rotation surfaces in 3-dimensional de Sitter space. J Geom 2004; 79: 156–168.
  • Milousheva V. General rotational surfaces inR4with meridians lying in two-dimensional planes. C R Acad Bulgare Sci 2010; 63: 339–348.
  • Moore C. Surfaces of rotation in a space of four dimensions. Ann Math 1919; 21: 81–93.
  • Moore C. Rotation surfaces of constant curvature in space of four dimensions. Bull Amer Math Soc 1920; 26: 454–460.