We might not be aware of it, but we are actually used to living in a curved, multidimensional Universe. In this episode theoretical physicist David Berman explains how, and he also dives into the world of string theory which predicts that the Universe has ten dimensions, some of which are hidden from our view. We first published this episode back in 2012, as part of our Science fiction, science fact.
You can also read the articles that accompany this podcast: Kaluza, Klein and their story of a fifth dimension and The ten dimensions of string theory.
There are not extra dimensions. Read "Against fantasy: In n no more than n" International Journal of Science and Resarch, Vo 3 Issue 5. May 2014.