position 4-vector of finite norm does not exist in curved spacetime

position 4-vector of finite norm does not exist in curved spacetime?[sudhakaran gopalan also known as g.sudhakaran,7/m.sc/physics/1964,iit,mad... the author of gr-qc/0106029 in xxx.lanl.gov and the paper 'mathematical philosophy of time in minkowskian space',published in IJERT]