ar X iv : m at h - ph / 9 90 50 25 v 1 3 1 M ay 1 99 9 Incompressible Fields in Riemannian Manifolds
نویسنده
چکیده
Incompressible fields are of special importance in elec-todynamics, fluid mechanics, and quantum mechanics. We shall derive a few expressions for such fields in a Riemannian manifold, and show how to generate an incompressible field from an arbitrary set of scalar functions. The concept of compressibility removing factors of an arbitrary vector field is introduced and utilized to obtain from an arbitrary vector field an incompresible one that has the same vector surface as the original field. A genral expression for a compressibility removing factor of a vector field is derived. 1. Introduction The equation which expresses that a vector field L has a zero divergence, divL = 0, appears in a number of areas of physics such as electrodynamics, fluid mechanics, and quantum mechanics. In fact two of Maxwell's equations, namely div
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