On a Special Class of Polynomial Surfaces with Pythagorean Normal Vector Fields

2012 ◽  
pp. 431-444 ◽  
Author(s):  
Miroslav Lávička ◽  
Jan Vršek
Keyword(s):  
Special Class ◽  
Vector Fields ◽  
Normal Vector

Immersions with non-zero normal vector fields

1992 ◽  
Vol 112 (2) ◽  
pp. 281-285 ◽  
Author(s):  
Bang-He Li ◽  
Gui-Song Li
Keyword(s):  
Vector Fields ◽  
Normal Vector ◽  
Homotopy Classes ◽  
Natural Action ◽  
Singularity Method ◽  
One To One ◽  
Regular Homotopy

Let M be a smooth n-manifold, X be a smooth (2n − 1)-manifold, and g:M → X be a map. It was proved in [6] that g is always homotopic to an immersion. The set of homotopy classes of monomorphisms from TM into g*TX, which is denoted by Sg, may be enumerated either by the method of I. M. James and E. Thomas or by the singularity method of U. Koschorke (see [1] and references therein). When the natural action of π1(XM, g) on Sg is trivial, for example, if X is euclidean, the set Sg is in one-to-one correspondence with the set of regular homotopy classes of immersions homotopic to g (see e.g. [4]).

scholarly journals Discrete Normal Vector Field Approximation via Time Scale Calculus

2020 ◽  
Vol 5 (1) ◽  
pp. 349-360
Author(s):  
Ömer Akgandüller ◽  
Sibel Paşalı Atmaca
Keyword(s):  
Time Scales ◽  
Vector Fields ◽  
Geometric Analysis ◽  
Field Approximation ◽  
Normal Vector ◽  
Normal Vector Field ◽  
Time Scale Calculus ◽  
Vertex Set ◽  
Rectangular Grids ◽  
Mimetic Discretization

AbstractThe theory of time scales calculus have long been a subject to many researchers from different disciplines. Beside the unification and the extension aspects of the theory, it emerge as a powerful tool for mimetic discretization process. In this study, we present a framework to find normal vector fields of discrete point sets in ℝ3 by using symmetric differential on time scales. A surface parameterized by the tensor product of two time scales can be analogously expressed as the vertex set of non-regular rectangular grids. If the time scales are dense, then the discrete grid structure vanishes. If the time scales are isolated, then the further geometric analysis can be executed by using symmetric dynamic differential. Moreover, we present an algorithmic procedure to determine the symmetric dynamic differential structure on the neighborhood of points in surfaces. Our results indicate that the method we present has good approximation to unit normal vector fields of parameterized surfaces rather than the Delaunay triangulation for some points.

scholarly journals On Pull-Back Bundle of Tensor Bundles Defined by Projection of The Cotangent Bundle

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Furkan Yildirim
Keyword(s):  
Special Class ◽  
Cotangent Bundle ◽  
Vector Fields ◽  
Complete Lift ◽  
Tensor Bundle

AbstractUsing projection (submersion) of the cotangent bundle T*M over a manifold M, we define a semi-tensor (pull-back) bundle tM of type (p,q). The aim of this study is to investigate complete lift of vector fields in a special class of semi-tensor bundle tM of the type (p,q). We also have a new example for good square in this work.

PROPER PROJECTIVE SYMMETRY IN SPHERICALLY SYMMETRIC STATIC SPACE–TIMES

2005 ◽  
Vol 14 (08) ◽  
pp. 1451-1463 ◽  
Author(s):  
GHULAM SHABBIR ◽  
M. AMER QURESHI
Keyword(s):  
Special Class ◽  
Vector Fields ◽  
Space Time ◽  
Spherically Symmetric ◽  
Direct Integration ◽  
Integration Techniques ◽  
Projective Vector ◽  
Static Space

A study of proper projective symmetry in spherically symmetric static space–times is given by using algebraic and direct integration techniques. It is shown that a special class of the above space–time admits proper projective vector fields.

Switching Dynamics of a Periodically Forced Discontinuous System With an Inclined Boundary

2007 ◽  
Author(s):  
Albert C. J. Luo ◽  
Brandon M. Rapp
Keyword(s):  
Dynamical System ◽  
Vector Fields ◽  
Normal Vector ◽  
Periodic Motions ◽  
Separation Boundary ◽  
Discontinuous System ◽  
Normal Vector Field ◽  
Periodically Driven ◽  
Switching Dynamics ◽  
Straight Line

This paper presents the switching dynamics of flow from one domain into another one in the periodically driven, discontinuous dynamical system. The simple inclined straight line boundary in phase space is considered as a control law for the dynamical system to switch. The normal vector-field product for flow switching on the separation boundary is introduced, and the passability condition of flow to the discontinuous boundary is presented. The sliding and grazing conditions to the separation boundary are presented as well. Using mapping structures, periodic motions of such a discontinuous system are predicted, and the local stability and bifurcation analysis are carried out. Numerical illustrations of periodic motions with grazing to the boundary and/or sliding on the boundary are given, and the normal vector fields are illustrated to show the analytical criteria.

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