- #1

cianfa72

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Hi,

consider an "half-cone" represented in Euclidean space ##R^3## in cartesian coordinates ##(x,y,z)## by: $$(x,y,\sqrt {x^2+y^2})$$

It does exist an homeomorphism with ##R^2## through, for instance, the projection ##p## of the half-cone on the ##R^2## plane. You can use ##p^{-1}## to get a

It seems good, but I've some problem with it because of lack of tangent plane on the apex with coordinates ##(0,0,0)## when we think it living in ##R^3##.

Can you help me ? thanks

consider an "half-cone" represented in Euclidean space ##R^3## in cartesian coordinates ##(x,y,z)## by: $$(x,y,\sqrt {x^2+y^2})$$

It does exist an homeomorphism with ##R^2## through, for instance, the projection ##p## of the half-cone on the ##R^2## plane. You can use ##p^{-1}## to get a

*differential*manifold structure on it.It seems good, but I've some problem with it because of lack of tangent plane on the apex with coordinates ##(0,0,0)## when we think it living in ##R^3##.

Can you help me ? thanks

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