I just checked in Baidu "covariant derivative", looked at first glance to know how it happens, it really is the content tensor.
Oh ……
Tensor do this thing, do a bunch of symbols out, in fact, no mystery, the basic principle is still the calculus, but a series of demands put tensor "package" has become a "tensor API", those arrows colon there are the words "covariant derivative", "covariant derivative" like symbols and the like are content API, can be considered a method parameters provided by the API, you go with the line.
Oh ...... I top with some of the terminology of computer programming,
Because the software industry is now popular to engage in this, this is called "abstraction layer", such as similar containers, and mathematics tensor, container is an abstraction layer on top of the operating system, is an abstract tensor calculus over layers, but these layers of abstraction cumbersome and complex, consuming learning costs, bound programmer (scientists) are fighting the explosive tension vitality productivity. More harm than good.
This is a disease, called "Abstraction Layer ills"
Now the software industry and the scientific community prevalence of this disease, which is closely associated with Western academic thought.