I have been reading Fundamentals of Differential Geometry by Serge Lang. In his treatment, the notion of sprays plays a central role. However, I rarely see this term in other books on the subject.
Although this is a soft question, I try to make clear my questions:
- Is spray a somewhat out-dated notion?
- What is the geometric meaning of sprays? (This name is suggestive but I don't have any intuition for it...)
- What are the advantages and disadvantages of using sprays?
- Can you suggest an alternative book whose treatment is similar to that of Lang's and which is modern and readable?
Thanks in advance!