الفهرس 
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Abstract
In this thesis, we present some results in complex analysis concerning Bedding of compact Kahler manifolds into a complex projective space and vanishing theorems for the cohomology groups on a complex manifold with strictly q-convex boundary. Indeed, we proved that:
If M is compact Kahler manifold of complex dimension n and its first Chern :lass is semi-positive at any point of M and of rank n -1 at one point of M, then M is projective algebraic.
2-Let M be a Kahler manifold of complex dimension n andX czc M be a strictly q-convex (q > 1). Let E be a holomorphic vector bundle of rank p > 1 over M. If E is Wakano semi-positive of type k over X, then we have
Hs(X,Qn(E)) = 0, fors>q,s>k,
and
H^(X,Q°(E*)) = 0, for s<n-q,s<n-k, and if E is Griffiths semi-positive of type k at any point of X, then we have Hs(X,Qr(E)) = 0, for r + s>n + k + p-l,s>q,”
and
H*(X,£2r(E*)) = 0, for r + s<n-k-p + l,s<n-q. Here, we denote by Hs(X,Qr(E)) the s-th cohomology group of X with Baefficients ?in the sheaf of the germs of E-valued holomorphic r-forms, Kc(X,Qr(E)) the s-th cohomology group with compact support in X with
■efficients in the sheaf of the germs of E-valued holomorphic r-forms and E* is the dual bundle of E.
This thesis consists of an introduction, three chapters, and a list of references, together with arabic and english summaries. Those can be summarized as follows:
Introduction.
It includes a quick hint for the purpose of this thesis and its contents. Chapter I.
It is an introductory chapter, which contains the basic definitions and results which will be used in later chapters.
Chapter II.
In this chapter we prove the embedding of some compact Kahler manifolds into a complex projective space PN (£) for some integer N.
Chapter III.
The rest of the results of this thesis are given in this chapter. In this chapter we gave a similar result of Grauert-Riemenschneider [11] with a feebler condition on the boundary and extend this result to the cohomology of type (r, s). Indeed, we replace the condition of hyper q-convexity on the boundary of X (in [11]) by the weaker condition of strict q-convexity to prove the following results: Let M be a Kahler manifold of complex dimension n and X cc M be a strictly q-»nvex (q > 1). Let E be a holomorphic vector bundle of rank p> 1 over M. If E is jjkano semi-positive of type k at any point of X, then
Hs(X, Qn (E)) = 0, for s > q, s > k,
H^(X,Q°(E*)) = 0, fors<n-q,s<n-k, and if E is Griffiths semi-positive of type k at any point of X, then Hs(X,Qr(E)) = 0, forr + s>n + k + p-l,s>q,
H*(X,fir(E*)) = 0, forr + s<n-k-p + l,s<n-q.