What's more general than Riemann space?
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From: Chip Eastham on 14 Jun 2010 01:16 On Jun 12, 7:04 pm, Edward Green <spamspamsp...(a)netzero.com> wrote: > What's more general than Riemann space? Apparently it results from > relaxing the requirement that there be a metric tensor, and is > conventionally denoted by a capital script letter which I cannot > decipher. What is likely the letter, and what is the space called? One level of generalization would be "manifold". Hard to say if that's what you are looking for from the vague mention of "a capital script letter". regards, chip
From: David Bernier on 14 Jun 2010 02:44 Chip Eastham wrote: > On Jun 12, 7:04 pm, Edward Green<spamspamsp...(a)netzero.com> wrote: >> What's more general than Riemann space? Apparently it results from >> relaxing the requirement that there be a metric tensor, and is >> conventionally denoted by a capital script letter which I cannot >> decipher. What is likely the letter, and what is the space called? > > One level of generalization would be "manifold". > > Hard to say if that's what you are looking for > from the vague mention of "a capital script > letter". Another direction is to study equivalence by projections, a kind of generalization of the study of conic sections, "geometry of shadows cast on a plane", i.e. projective geometry: < http://en.wikipedia.org/wiki/Projective_geometry > , though Coxeter's text might be better. David Bernier
From: Igor on 14 Jun 2010 12:43 On Jun 13, 10:49 am, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote: > "Igor" <thoov...(a)excite.com> wrote in message > > news:bd35ebdd-08a8-42eb-abf7-614afe8a7eb2(a)e5g2000yqn.googlegroups.com... > On Jun 12, 8:04 pm, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote: > > > "Edward Green" <spamspamsp...(a)netzero.com> wrote in message > > >news:4c04f840-cc88-437e-b4e0-ffe904ca73fc(a)35g2000vbj.googlegroups.com... > > | What's more general than Riemann space? > > > Euclidean space. > > BUZZ!!! Euclidean space is a subset of Riemann space. No cookie for > you. > ================================================= > BUZZ!!! > Riemann space has a different postulate to Euclidean space. > http://en.wikipedia.org/wiki/Parallel_postulate There is NO parallel postulate in Riemann space. You lose. > BUZZ!!! > I would claim that Euclidean space was a subset of > Lobachevsky space if I was as ignorant as you. No. Lobachevsky space is another subset of Riemann. You lose again. > BUZZ!!! > You couldn't even buy a clue, let alone a cookie. And you are not a fricking engineer. If you are, you must have bought your degree. You sure as hell didn't earn one.
From: adamk on 14 Jun 2010 12:38 > On Jun 12, 4:04 pm, Edward Green > <spamspamsp...(a)netzero.com> wrote: > > What's more general than Riemann space? Apparently > it results from > > relaxing the requirement that there be a metric > tensor, and is > > conventionally denoted by a capital script letter > which I cannot > > decipher. What is likely the letter, and what is > the space called? > > A round or spherical 3D space curve. This is > spherical Riemannian > geometry applied to gravity. It also applies to > aether but people do > not want to believe. > > The old parabolic geometry needs to be corrected by a > spherical one. > Even for cosmology but up one dimension when the > aether closes the > universe. > > MItch Raemsch Why do you feel the need to inflict your stupidity and complete ignorance on everyone else.?
From: Igor on 14 Jun 2010 18:06
On Jun 14, 1:12 pm, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote: > "Igor" <thoov...(a)excite.com> wrote in message > > news:83cc04c2-eb0a-4041-9a36-3eea4365d424(a)a30g2000yqn.googlegroups.com... > On Jun 13, 10:49 am, "Androcles" <Headmas...(a)Hogwarts.physics_z> > wrote: > > > > > "Igor" <thoov...(a)excite.com> wrote in message > > >news:bd35ebdd-08a8-42eb-abf7-614afe8a7eb2(a)e5g2000yqn.googlegroups.com... > > On Jun 12, 8:04 pm, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote: > > > > "Edward Green" <spamspamsp...(a)netzero.com> wrote in message > > > >news:4c04f840-cc88-437e-b4e0-ffe904ca73fc(a)35g2000vbj.googlegroups.com.... > > > | What's more general than Riemann space? > > > > Euclidean space. > > > BUZZ!!! Euclidean space is a subset of Riemann space. No cookie for > > you. > > ================================================= > > BUZZ!!! > > Riemann space has a different postulate to Euclidean space. > >http://en.wikipedia.org/wiki/Parallel_postulate > > There is NO parallel postulate in Riemann space. You lose. > > ============================================ > BUZZ!!! > Lines of longitude are postulated to be parallel at the equator. That's only because a sphere is locally Euclidean. All surfaces are. Non-Euclidean geometries were only generated AFTER the parallel postulate was removed. Bringing it back only places you back in Euclid's realm. Hence, Euclidean is a subset of non-Euclidean. Try to let that sink in through your senility. |