DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE

We review part of the classical theory of curves and surfaces in 3-dimensional Lorentz-Minkowski space. We focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.

[1]  A. Alexandrov.  A characteristic property of spheres , 1962 .

[2]  B. O'neill.  Semi-Riemannian Geometry With Applications to Relativity , 1983 .

[3]  N. Koike,et al.  CONGRUENCE THEOREMS FOR PROPER SEMI- RIEMANNIAN HYPERSURFACES IN A REAL SPACE FORM , 1987 .

[4]  Vertex theorems for capillary drops on support planes , 1997, math/9707217.

[5]  Huili Liu,et al.  Translation surfaces with constant mean curvature in 3-dimensional spaces , 1999 .

[6]  W. Kühnel.  Differential Geometry: Curves - Surfaces - Manifolds , 2002 .

[7]  Robert Finn,et al.  Equilibrium Capillary Surfaces , 1985 .

[8]  Osamu Kobayashi.  Maximal Surfaces in the 3-Dimensional Minkowski Space $L^3$ , 1983 .

[9]  K. Nomizu,et al.  Surfaces of revolution with constant mean curvature in Lorentz-Minkowski space , 1984 .

[10]  Rafael L'opez.  Differential Geometry of Curves and Surfaces in Lorentz-Minkowski space Mini-Course taught at the Instituto de Matemática e Estat́ıstica ( IME-USP ) , 2008, 0810.3351.

[11]  Sungwook Lee,et al.  NULL CURVES IN MINKOWSKI 3-SPACE , 2008 .

[12]  P. Mira,et al.  Helicoidal Maximal Surfaces in Lorentz-Minkowski Space , 2003 .

[13]  B. O'neill.  Elementary Differential Geometry , 1966 .

[14]  Johannes C. C. Nitsche,et al.  Stationary partitioning of convex bodies , 1985 .

[15]  Rafael López,et al.  Constant Mean Curvature Surfaces with Boundary , 2013 .

[16]  J. Walrave,et al.  Curves and surfaces in Minkowski space , 1995 .

[17]  M. Magid.  Lorentzian isoparametric hypersurfaces , 1985 .

[18]  R. López.  Constant mean curvature hypersurfaces foliated by spheres , 1999 .

[19]  M. Athanassenas,et al.  A variational problem for constant mean curvature surfaces with free boundary. , 1987 .

[20]  Sung-Ho Park,et al.  Every ring type spanner in a wedge is spherical , 2005 .

[21]  T. I. Vogel.  Stability of a liquid drop trapped between two parallel planes , 1987 .

[22]  A. Ferrández,et al.  Null Helices in Lorentzian Space Forms , 2001 .

[23]  Manfredo P. do Carmo,et al.  Differential geometry of curves and surfaces , 1976 .

[24]  L. K. Graves,et al.  Codimension one isometric immersions between Lorentz spaces , 1979 .

[25]  W. Kühnel,et al.  Ruled Weingarten surfaces in Minkowski 3-space , 1999 .

[26]  Sung-Ho Park,et al.  Capillary surfaces in a convex cone , 2011 .

[27]  J. Clelland.  Totally quasi-umbilic timelike surfaces in $\mathbb{R}^{1,2}$ , 2010, 1006.4380.