Sweeping Surfaces in theThree-Dimensional Lie Group
نویسندگان
چکیده
This paper investigated the rotation minimizing frames that are related to space curves and sweeping surfaces traced by these in three-dimensional Lie group. Then, sufficient necessary conditions for surface be a developable ruled were obtained. In particular, we mostly focused on study of resulting is cylinder, cone, or tangent surface. Meanwhile, support results paper, some illustrative examples presented.
منابع مشابه
Translation invariant surfaces in the 3-dimensional Heisenberg group
In this paper, we study translation invariant surfaces in the 3-dimensional Heisenberg group $rm Nil_3$. In particular, we completely classify translation invariant surfaces in $rm Nil_3$ whose position vector $x$ satisfies the equation $Delta x = Ax$, where $Delta$ is the Laplacian operator of the surface and $A$ is a $3 times 3$-real matrix.
متن کاملSweeping and Maintaining Two-Dimensional Arrangements on Surfaces
We introduce a general framework for processing a set of curves defined on a continuous two-dimensional parametric surface, while sweeping the parameter space. A major goal of our work is to maximize code reuse in implementing algorithms that employ the prevalent sweep-line paradigm, and consequently to minimize the effort needed to extend the implementation of the paradigm to various surfaces ...
متن کاملtranslation invariant surfaces in the 3-dimensional heisenberg group
in this paper, we study translation invariant surfaces in the 3-dimensional heisenberg group $rm nil_3$. in particular, we completely classify translation invariant surfaces in $rm nil_3$ whose position vector $x$ satisfies the equation $delta x = ax$, where $delta$ is the laplacian operator of the surface and $a$ is a $3 times 3$-real matrix.
متن کاملVariationality of Four-Dimensional Lie Group Connections
This paper gives a comprehensive analysis of the inverse problem of Lagrangian dynamics for the geodesic equations of the canonical linear connection on Lie groups of dimension four. Starting from the Lie algebra, in every case a faithful four-dimensional representation of the algebra is given as well as one in terms of vector fields and a representation of the linear group of which the given a...
متن کاملSweeping of three-dimensional objects
The basic problem which this paper addresses is the following: given an arbitrary three-dimensional object, which moves along an arbitrary path (possibly rotating as it does so), to compute the volume swept out by the solid object as it moves, or in other words, to find the new solid volume which represents all of the points in space which the object has occupied at some time during the motion....
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: Symmetry
سال: 2022
ISSN: ['0865-4824', '2226-1877']
DOI: https://doi.org/10.3390/sym14040698