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If we suppose the following 8-dimensional manifold given by

$$a_1=cos(x)cos(y)cos(z)$$

$$a_2=cos(x)cos(y)sin(z)$$

$$a_3=cos(x)sin(y)cos(z)$$

$$a_4=cos(x)sin(y)sin(z)$$

$$a_5=sin(x)cos(y)cos(z)$$

$$a_6=sin(x)cos(y)sin(z)$$

$$a_7=sin(x)sin(y)cos(z)$$

$$a_8=sin(x)sin(y)sin(z)$$

Then obviously it's a 3 sphere and verifying the metric is euclidean is not so hard.

Since the metric of this 3sphere is euclidean there would be no way to detect for a R^3 lander if he lives in fact in such a high dimensional hypersphere ? (Or maybe by solving EFE in higher dimension and check gravitation experimentally ?)

$$a_1=cos(x)cos(y)cos(z)$$

$$a_2=cos(x)cos(y)sin(z)$$

$$a_3=cos(x)sin(y)cos(z)$$

$$a_4=cos(x)sin(y)sin(z)$$

$$a_5=sin(x)cos(y)cos(z)$$

$$a_6=sin(x)cos(y)sin(z)$$

$$a_7=sin(x)sin(y)cos(z)$$

$$a_8=sin(x)sin(y)sin(z)$$

Then obviously it's a 3 sphere and verifying the metric is euclidean is not so hard.

Since the metric of this 3sphere is euclidean there would be no way to detect for a R^3 lander if he lives in fact in such a high dimensional hypersphere ? (Or maybe by solving EFE in higher dimension and check gravitation experimentally ?)

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