Classification of surfaces in which are centroaffine-minimal and equiaffine-minimal.
Liu, Huili (1996)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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Liu, Huili (1996)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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Ekici, Cumali, Ünlütürk, Yasin, Dede, Mustafa, Ryuh, B.S. (2008)
Mathematical Problems in Engineering
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Roussos, Ioannis M. (1988)
Publications de l'Institut Mathématique. Nouvelle Série
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Thomas Friedrich (1997)
Archivum Mathematicum
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Using the Cartan method O. Boruvka (see [B1], [B2]) studied superminimal surfaces in four-dimensional space forms. In particular, he described locally the family of all superminimal surfaces and classified all of them with a constant radius of the indicatrix. We discuss the mentioned results from the point of view of the twistor theory, providing some new proofs. It turns out that the superminimal surfaces investigated by geometers at the beginning of this century as well...
Udo Simon, Konrad Voss, Luc Vrancken, Martin Wiehe (2002)
Banach Center Publications
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We investigate pairs of surfaces in Euclidean 3-space with the same Weingarten operator in case that one surface is given as surface of revolution. Our local and global results complement global results on ovaloids of revolution from S-V-W-W.
Orbay, Keziban, Kasap, Emin, Aydemir, İsmail (2009)
Mathematical Problems in Engineering
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Georgi Ganchev, Velichka Milousheva (2010)
Open Mathematics
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In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes...
Rafael López, Esma Demir (2014)
Open Mathematics
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We classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.
M. A. Magid (2004)
Annales Polonici Mathematici
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Lorentzian surfaces in Lorentz three-space are studied using an indefinite version of the quaternions. A classification theorem for Bonnet pairs in Lorentz three-space is obtained.
Harold Rosenberg (1991-1992)
Séminaire Bourbaki
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M. P. Dussan, M. Magid (2010)
Annales Polonici Mathematici
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We characterize the Christoffel pairs of timelike isothermic surfaces in the four-dimensional split-quaternions. When restricting the receiving space to the three-dimensional imaginary split-quaternions, we establish an equivalent condition for a timelike surface in ℝ³₂ to be real or complex isothermic in terms of the existence of integrating factors.