As you may know, the metric tensor for 3D spherical coordinates is as follows: g11= 1 g22= r2 g33= r2sin2(θ) Now, the Minkowski metric tensor for spherical coordinates is this: g00= -1 g11= 1 g22= r2 g33= r2sin2(θ) In both of these metric tensors, all other elements are 0. Now, the only obvious difference between the two metric tensors is the fact that the Minkowski version has a -1 in it and a temporal row and column. The first metric tensor represents just flat space, while the second one represents flat space time. Now, in my recent studies of curvature, I was wondering if you could just add a -1 along with a temporal row and column to the metric tensor of the 3-sphere in order to make it represent a spherically curved 4 dimensional space time (just as adding a -1 and a temporal row/column to the 3D spherical coordinates metric tensor creates a 4D metric tensor that represents flat space-time). Here is what I mean: This is the metric tensor for the 3-sphere: g11=r2sin2(ø)sin2(ψ) g22=r2sin2(ψ) g33=r2 The rest of the elements are 0. As for my coordinate labels: x1=θ x2=ø x3=ψ And now, here is what I mean when I mention "adding a -1 and a temporal row/column to the metric tensor of the 3-sphere": g00= -1 g11=r2sin2(ø)sin2(ψ) g22=r2sin2(ψ) g33=r2 The rest of the elements are 0. As you can see here, I just added a -1 to the 3-sphere metric tensor just as the Minkowski metric tensor for spherical coordinates adds a -1 to the metric tensor of 3D spherical coordinates. Will adding this -1 to the 3-sphere's metric tensor make this metric represent spherically curved space time as a result?