I hear that environment variable about default directory for head file and library file
are C_INCLUDE_PATH and LD_LIBRARY_PATH,but I echo $LD_LIBRARY_PATH and
echo $C_INCLUDE_PATH,they are none,what are they?
LD_LIBRARY_PATH is just an additional variable. If it is set, then the paths specified in it will be added to the current shared libraries. All "default" libraries (that exist on a system and are registered) are managed by ldconfig, which generates /etc/ld.so.cache out of standard paths like /lib, /lib64, /usr/lib ...
I can't tell you about C_INCLUDE_PATH since I don't know anything about this one, but I think it may behave the same way.