The speed of light in vacuum is expected to be a universal constant. Now let us review the fact in the light of the following situation: We consider three different points A,B and C in curved space-time(in vacuum).Observers stationed at A and B see a light ray flashing across an small spatial interval at C. Now the length of the spatial interval at C is same for the two observers. But what about the time interval?.The coordinate separation for the two time intervals is the same for both the observers.But the physical separations may by different because of the differences in the values of g(00) at A and B. We must take note of two facts very carefully: 1)The observers have theirs clocks at the points A and B and the physical intervals measured by these clocks are dependent on the values of g(00) at these points. 2) The length of the spatial interval at C as measured by A and B does not depend on the values of g(mu,nu) at A and B. It depends on the value of g(mu,nu) at C only. This implies that the speed of light as measured by the two observers should be different. The uploaded file discusses the above problem.