Integration of Complex Vector Fields
نویسنده
چکیده
(1.3) Lku = 0, k = 1,. . . , m. Any function u satisfying all the above equations must also satisfy the equations (1.4) [Lk9 Lh]u = LkLhu LhLku = 0. Thus it is reasonable to assume that the space spanned by the vector fields Lu..., Lm is closed under the bracket operation. Condition A. This condition is satisfied if (1.5) [Lk,IJ = I 4 ^ j where the a^6C°°((7). From (1.2) we obtain [Lk,Lh]u = Lkfh -LJk and hence (1.5) yields (1.6) Lkfh Lhfk = X a{hfj, \^k<h^m.
منابع مشابه
Local and global integration of discrete vector fields
This paper deals with the design of evaluation procedures for surface integration techniques. We start with a survey of existing integration techniques which calculate height maps from dense gradient fields. There are a few proposals of local integration methods [2, 4, 11, 9], and two proposals for global optimization [6, 3]. The examined algorithms perform well for curved objects but unsatisfa...
متن کاملHarmonicity and Minimality of Vector Fields on Lorentzian Lie Groups
We consider four-dimensional lie groups equipped with left-invariant Lorentzian Einstein metrics, and determine the harmonicity properties of vector fields on these spaces. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. We also classify vector fields defining harmonic maps, and calculate explicitly the energy of t...
متن کاملSome vector fields on a riemannian manifold with semi-symmetric metric connection
In the first part of this paper, some theorems are given for a Riemannian manifold with semi-symmetric metric connection. In the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. We obtain some properties of this manifold having the vectors mentioned above.
متن کاملAbsorbed Dose Calculation In Irregular Blocked Radiation Fields: Evaluation of Clarkson’s Sector Integration Method for Radiation Fields Commonly Used in Conventional Radiotherapy
Introduction: Irregular/blocked fields are routinely used in radiotherapy. The doses of these fields are usually calculated by means of equivalent square method that is inherently prone to uncertainty. On the other hand, Clarkson’s sector integration method is a dose calculation method which offers far better accuracy in dose calculation of irregular fields. The Scatter Air Ratio (SAR) of an in...
متن کاملConcurrent vector fields on Finsler spaces
In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fi...
متن کاملShape deformations based on vector fields
This thesis explores applications of vector field processing to shape deformations. We present a novel method to construct divergence-free vector fields which are used to deform shapes by vector field integration (Chapter 2). The resulting deformation is volume-preserving and no self-intersections occur. We add more controllability to this approach by introducing implicit boundaries (Chapter 3)...
متن کامل