The Structure Of Projective Varieties And Its Vector Bundles

In this paper, The main purpose of this paper is to characterizations the structure of a hyperquadric Qn and an ample vector bundle on a varieties, This paper shows a main result:Let X be a smooth projective variety of dimension n and E an ample vector bundle with rank r< n.Assume that numerically effective value of E over X is n/r and that the picard number of X is one,then X is a hyperquadric Qn,and X is a direct sum of line bundles OQn(1).