Effective vanishing theorems for ample and globally generated vector bundles

By proving an integral formula of the curvature tensor of $E\text{ts}\det E$, we observe that the curvature tensor of $E\text{ts}\det E$ is very similar to that of a line bundle and obtain certain new Kodaira-Akizuki-Nakano type vanishing theorems for vector bundles. As special cases, we deduce vanishing theorems for ample, nef and globally generated vector bundles by analytic method instead of the Leray-Borel-Le Potier spectral sequence.