This occurs on Mac OS X 10.7.4, on git versions 1.7.10.2 (Apple Git-33) and 1.7.11.3.
Steps:
1. Create or clone a repository to an absolute path that contains spaces.
2. Add a submodule to the repository, if it does not already have one.
3. Within that submodule, attempt to add another submodule.
The result is an error "fatal: Not a git repository", followed by the relative path to the submodule directory within .git/modules of the top-level repository.
Similarly, using "git submodule update --init --recursive" in a freshly-cloned repository that matches the above configuration will fail with the same error. "git clone --recursive" does not seem to suffer from the same problem at clone time, but will still fail to add recursive submodules.
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Justin Spahr-Summers