In addition to being used bases<...>in the second argument specified as indicated by Autopulated, I think you also want to specify boost::noncopyableas the third argument to the template, for example.
bp::class_<LogManager, bp::bases<boost::serialization::singleton<LogManager> >, boost::noncopyable>("LogManager", bp::no_init)
Edit : In addition, you need to have a class declaration for any of the listed base classes, for example.
bp::class_<boost::serialization::singleton<LogManager>, boost::noncopyable>("Singleton", bp::no_init)
, boost::serialization::singleton<LogManager>, . , , , LogManager:
bp::class_<LogManager, boost::noncopyable>("LogManager", bp::no_init)