Vanishing theorems on (l|k)-strong Kahler manifolds with torsion

We derive sufficient conditions for the vanishing of plurigenera, p(m)(J), m > 0, on compact (l vertical bar k)-strong, omega(l) Lambda partial derivative partial derivative omega(k) = 0, Kahler manifolds with torsion. In particular, we show that the plurigenera of closed (l vertical bar k)-strong manifolds, k < n - 1, for which hol(<(del)over cap>) subset of SU(n) vanish, where (del) over cap is the Hermitian connection with skew-symmetric torsion. As a consequence all generalized k-Gauduchon manifolds for which hol((del) over cap) subset of SU(n) do not admit holomorphic (n, 0) forms. Furthermore we show that all conformally balanced, (l vertical bar k)-strong Miller manifolds with torsion, k not equal n - 1, are Kahler. We also give several examples of (l vertical bar k)-strong Kahler and Calabi-Yau manifolds with torsion. (C) 2013 Elsevier Inc. All rights reserved.