Hi everyone; I'm new to both PF and GR, so please bear with me if I'm not being very clear, or using standard syntax and such. Here is my question. Given a vector v^a, the covariant derivative is defined as v^a _;b = v^a _,b + v^c GAMMA^a _bc. (here I'm using ^ before upper indices and _ before lower indices). The object I'm interested in now is v^a;b (where the whole thing a;b is upper). Is this called the contravariant derivative? Is there a similar definition in terms of the Christoffel symbol? or can we only obtain it from contracting v^a _;b with the metric? I can't seem to find the definition of this object in any books, and when I try to do my calculation via contraction with the metric, I'm getting the wrong answer. Thanks.