## Plasma Trajectories on Gravitational Fields via Exterior Differential Forms

Dr. Logman Abd Allah Saeed Hamed,2010, Plasma Trajectories on Gravitational Fields via Exterior Differential Forms ,Journal of Science and Technology,11 (2) ,pp:0-0

Authors:

By Dr. Logman Abd Allah Saeed Hamed,

Year:

2010

Keywords

Exterior differential system; Riemannian configuration manifold; covariant force law; Geodesic spray.

Abstract

Recall that the curve at a point of an n manifold is a -map from an open interval into such that and . For such a curve we assign a tangent vector at each point , by .
So an integral curve (or flow line) of the tangent vector–field is a paramet- erized curve satisfying the following condition
(1)
Where the maximal integral curve of through is a parameterized curve satisfying [8]:
(i)
(ii) If is any other parameterized curve in satisfying (i) and (1), then and for all .
The velocity of the parameterized curve is a vector–field along defined by ,
and its speed defined by for all .

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