Handout Five: Vector Fields
نویسنده
چکیده
We have already studied several kinds of functions of several variables: vector valued functions of a scalar variable – i.e., parameterized curves in the plane and in space; scalar-valued functions of two or more variables (the case of two variables z = f(x, y) giving the graph of a surface in space; and functions from the plane to space, parameterized surfaces. Here we consider functions V from the plane to itself and from space to itself, which are called vector fields.
منابع مشابه
Some Multilinear Algebra over Fields Which I Understand
Most of what is discussed in this handout extends verbatim to all fields with the exception of the description of the Exterior and Symmetric Algebras, which requires more care in non-zero characteristic. These differences can be easily accounted for except for the properties of the Exterior Algebra in characteristic 2, which require a significant amount of work to understand. I will, however, a...
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 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 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 کاملInformed consent when prescribing medication: a randomized controlled trial.
OBJECTIVES/HYPOTHESIS To determine patient recall of specific risks associated with medication prescription and whether or not handouts are an effective tool to augment the informed consent process. STUDY DESIGN Double-blinded, randomized, controlled trial. METHODS Informed consent for prednisone prescriptions was studied by comparing the effect of a verbal discussion (describing 10 specifi...
متن کامل