why i am asking this question is that, i thought that photon takes no time to reach the earth or any other place in the universe due to length contraction. the reason for this is space wraps completly from starting to the end making the displacement zero, which is due to the value of $c$. the velocity of space around it from its reference frame.
Massless elementary particles like the photon are traveling at the speed of light in vacuum when measured locally.
Viewed from earth, though, it takes for the photon to reach earth from the sun approx 8 minutes.
Massless particles do not travel at infinite speeds, they have a finite speed, c, and since the distance is finite to, the time it will take them to reach earth is not zero, in this case it is approx. 8 minutes (when viewed from earth).
Now the misunderstanding with photons since they are massless, is that they do not have a reference frame. You could not say, let's imagine we are traveling with the photon, what would we see, how much time would pass, and questions like that.
If you really want to imagine what it can be like for the photon, you have to start doing math. What does math tell us?
Math tells us, that (if you could travel with the photon), the time elapsed between the photons emission in the sun and its absorption on earth, would be 0.
Photons, being massless, based on math, do not experience time like we do, their speed in the time dimension is 0.
In GR and in math we call this a lightlike worldline.
It is usually hard to understand, because massless particles are at one end of the scale, and in math some divisions would go to infinity regarding their speeds, and other attributes, meaning they are not countable. That is why we cannot talk about a reference frame for the photon.
It would be much easier for you if you would try to figure out, what would it be like if you would travel with a neutrino from the sun to earth.
Neutrinos have mass, and their speed is just a little less then c, but still their calculations would be relativistic, as close as you can get to speed c.
Now in that case, length contraction would cause the distance seen from the neutrino's frame, to be almost 0. Time on the neutrino's frame would pass very slowly, so for the neutrino (in the neutrino's frame), it would be much less then 8 minutes to get to earth.
This case is almost the photon's case, you see but it is still countable, so it makes you easier to understand what would happen if there was a frame for the photon.
So I will not try to answer your question in the title. "Does the space and time wraping depends on the relative velocity of frame of reference?"
Now what you are thinking of, is warping of spacetime, as you call it, that as per SR and GR is time dilation and length contraction. I just showed you that yes, relativistic speeds, like the one the neutrino is traveling at, will cause time dilation and length contraction.