T -SYMMETRICAL TENSOR DIFFERENTIAL FORMS WITH LOGARITHMIC POLES ALONG A HYPERSURFACE SECTION

. The aim of this paper is to investigate T -symmetrical tensor differ-ential forms with logarithmic poles on the projective space P N and on complete intersections Y ⊂ P N . Let H ⊂ P N ,N ≥ 2, be a nonsingular irreducible algebraic hypersurface which implies that D = H is a prime divisor in P N . The main goal of this paper is the study of the locally free sheaves Ω T P N (log D ) and the calculation of their cohomology groups. In addition, for complete intersections Y ⊂ P N we give some vanishing theorems and recursion formulas.