What's more general than Riemann space?
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From: Edward Green on 14 Jun 2010 18:47 On Jun 14, 1:16 am, Chip Eastham <hardm...(a)gmail.com> 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". > > regards, chip D.F. Lawden, "Introduction to Tensor Calculus, Relativity and Cosmology", p.89, last line before section 31, should you happen to have a copy. Sorry I lack the technology to scan the thing to a web link.
From: Androcles on 14 Jun 2010 18:49 "Igor" <thoovler(a)excite.com> wrote in message news:2853b0ef-2239-4ac6-be37-d76e8fce12c7(a)8g2000vbg.googlegroups.com... 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. ============================================== Only, huh? Non-Euclidean geometries were only generated AFTER the parallel postulate was removed. =============================================== BZZZZZZZZT!!!!!! Riemann's parallel postulate: If a straight line crossing two straight lines makes the interior angles equal to two right angles, the two straight lines, if extended indefinitely, eventually MEET. Lobachevsky's parallel postulate: If a straight line crossing two straight lines makes the interior angles equal to two right angles, the two straight lines, if extended indefinitely, eventually DIVERGE. You can't distinguish Lobachevsky's geometry from Riemann's geometry without it. That's only because you are locally a dumbfuck.
From: eric gisse on 14 Jun 2010 19:31 Igor wrote: [...] > And you are not a fricking engineer. If you are, you must have bought > your degree. You sure as hell didn't earn one. It is my personal opinion that Androcles' only interaction with science and engineering was through management of those that could actually do it.
From: BURT on 14 Jun 2010 20:29 On Jun 14, 3:47 pm, Edward Green <spamspamsp...(a)netzero.com> wrote: > On Jun 14, 1:16 am, Chip Eastham <hardm...(a)gmail.com> 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". > > > regards, chip > > D.F. Lawden, "Introduction to Tensor Calculus, Relativity and > Cosmology", p.89, last line before section 31, should you happen to > have a copy. Sorry I lack the technology to scan the thing to a web > link. Riemann space is Riemann time. Mitch raemsch
From: Chip Eastham on 14 Jun 2010 22:19
On Jun 14, 6:47 pm, Edward Green <spamspamsp...(a)netzero.com> wrote: > On Jun 14, 1:16 am, Chip Eastham <hardm...(a)gmail.com> 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". > > > regards, chip > > D.F. Lawden, "Introduction to Tensor Calculus, Relativity and > Cosmology", p.89, last line before section 31, should you happen to > have a copy. Sorry I lack the technology to scan the thing to a web > link. Found it in Google Books, which provides a limited preview. That is a script S, with subscript N for the "local" dimension. I believe that the author is talking about manifolds, based on the quick glance into the next section where "coordinate frames" of S_N are discussed. regards, chip |