Differential geometry of spherical and ruled manifolds in threedimensional Euclidean space. I.
نویسندگان
چکیده
منابع مشابه
Characterizations of Slant Ruled Surfaces in the Euclidean 3-space
In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...
متن کاملStructure and characterization of ruled surfaces in Euclidean 3-space
Keywords: Ruled surface Structure function Pitch function Angle function of pitch Weingarten surface Binormal ruled surface a b s t r a c t In this paper, using the elementary method we study ruled surfaces, the simplest foliated submanifolds, in Euclidean 3-space. We define structure functions of the ruled surfaces, the invariants of non-developable ruled surfaces and discuss geometric propert...
متن کاملCyclic and ruled Lagrangian surfaces in complex Euclidean space
We study those Lagrangian surfaces in complex Euclidean space which are foliated by circles or by straight lines. The former, which we call cyclic, come in three types, each one being described by means of, respectively, a planar curve, a Legendrian curve in the 3-sphere or a Legendrian curve in the anti-de Sitter 3-space. We describe ruled Lagrangian surfaces and characterize the cyclic and ru...
متن کاملSpherical Functions on Euclidean Space
We study special functions on euclidean spaces from the viewpoint of riemannian symmetric spaces. Here the euclidean space En = G/K where G is the semidirect product Rn · K of the translation group with a closed subgroup K of the orthogonal group O(n). We give exact parameterizations of the space of (G,K)–spherical functions by a certain affine algebraic variety, and of the positive definite on...
متن کاملSpherical Submanifolds of a Euclidean Space
A1 and A2 being arbitrary constants. A natural generalization of this question to higher dimensions could be: ‘given an isometric immersion ψ : Mn → Rn+2 of a compact n-dimensional Riemannian manifold (Mn, g), obtain conditions for ψ(Mn) ⊂ Sn+1(c), where Sn+1(c) is the sphere of constant curvature c’. We write ψT , ψ⊥ as tangential and normal components of the position vector ψ in Rn+p and show...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky
سال: 1983
ISSN: 0528-2195
DOI: 10.21136/cpm.1983.118181