Gravitational anomalies in higher dimensional Riemann Cartan space

By applying the covariant Taylor expansion method of the heat kernel, the covariant Einstein anomalies associated with a Weyl fermion of spin \frac{1}{2} in four-, six- and eight-dimensional Riemann Cartan space are manifestly given. Many unknown terms with torsion tensors appear in these anomalies. The Lorentz anomaly is intimately related to the Einstein anomaly even in Riemann Cartan space. The explicit form of the Lorentz anomaly corresponding to the Einstein anomaly is also obtained.