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Classification of curves up to affine transformation in a finite dimensional space was studied by some different methods. In this paper, we achieve the exact formulas of affine invariants via the equivalence problem and in the view of Cartans lemma and then, state a necessary and sufficient condition for classification of n--Curves.
This paper is devoted to the complete classification of space curves under affine transformations in the view of Cartans theorem. Spivak has introduced the method but has not found the invariants. Furthermore, for the first time, we propound a necess
We construct a sequence of commuting central affine curve flows on $R^nbackslash 0$ invariant under the action of $SL(n,R)$ and prove the following results: (a) The central affine curvatures of a solution of the j-th central affine curve flow is a
An affine manifold is said to be geodesically complete if all affine geodesics extend for all time. It is said to be affine Killing complete if the integral curves for any affine Killing vector field extend for all time. We use the solution space of
We describe all affine maps from a Riemannian manifold to a metric space and all possible image spaces.
We discuss new sufficient conditions under which an affine manifold $(M, abla)$ is geodesically connected. These conditions are shown to be essentially weaker than those discussed in groundbreaking work by Beem and Parker and in recent work by Alexan