منابع مشابه
On linear Weingarten surfaces
In this paper we study surfaces in Euclidean 3-space that satisfy a Weingarten condition of linear type as κ1 = mκ2 + n, where m and n are real numbers and κ1 and κ2 denote the principal curvatures at each point of the surface. We investigate the possible existence of such surfaces parametrized by a uniparametric family of circles. Besides the surfaces of revolution, we prove that not exist mor...
متن کاملLinear Weingarten Surfaces in R
In this paper we study properties of linear Weingarten immersions and graphs related to non-existence problems and behaviour of its curvatures. The main results are obtained giving a harmonic representation of linear Weingarten surfaces and by proving optimal estimates of the height and curvatures that the immersion must satisfy, characterizing the spherical caps as the only ones achieving thes...
متن کاملEquiaffine Characterization of Lagrangian Surfaces in R
For non-degenerate surfaces in R, a distinguished transversal bundle called affine normal plane bundle was proposed in [8]. Lagrangian surfaces have remarkable properties with respect to this normal bundle, like for example, the normal bundle being Lagrangian. In this paper we characterize those surfaces which are Lagrangian with respect to some parallel symplectic form in R. Mathematics Subjec...
متن کاملOn the Invariant Theory of Weingarten Surfaces in Euclidean Space
We prove that any strongly regular Weingarten surface in Euclidean space carries locally geometric principal parameters. The basic theorem states that any strongly regular Weingarten surface is determined up to a motion by its structural functions and the normal curvature function satisfying a geometric differential equation. We apply these results to the special Weingarten surfaces: minimal su...
متن کاملParabolic Weingarten surfaces in hyperbolic space
A surface in hyperbolic space H 3 invariant by a group of parabolic isometries is called a parabolic surface. In this paper we investigate parabolic surfaces of H 3 that satisfy a linear Weingarten relation of the form aκ1 + bκ2 = c or aH + bK = c, where a, b, c ∈ R and, as usual, κi are the principal curvatures, H is the mean curvature and K is de Gaussian curvature. We classify all parabolic ...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1987
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1987.102185