Blogs about: Geodesics
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Hopf-Rinow II and an application
Now, let’s finish the proof of the Hopf-Rinow theorem (the first one) started yesterday. We need to show that given a Riemannian manifold which is a metric space , the existence of arbitrary geo… more →
Delta Epsilons
Geodesic equation: 2-d polar coordinates
wrote 1 month ago: Reference: Moore, Thomas A., A General Relativity Workbook, University Science Books (2013) – … more →
Geodesic equation: geodesics on a sphere
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wrote 1 month ago: Reference: Moore, Thomas A., A General Relativity Workbook, University Science Books (2013) – … more →
Geodesics: paths of longest proper time
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wrote 1 month ago: Reference: Moore, Thomas A., A General Relativity Workbook, University Science Books (2013) – … more →
Four-point CAT(0) condition
wrote 2 months ago: The definition of a metric space guarantees that if we pick three points from it, we can draw a tria … more →
Three hyperbolic metrics
wrote 5 months ago: Up to a constant factor, there is just one conformally invariant Riemannian metric on the disk . Ind … more →
How Dense?
wrote 9 months ago: In the last post I talked about the physics and considerations behind the gravity train. A crucial p … more →
The Relativistic Theory of Gravitation - Logunov, Mestvirishvili
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wrote 10 months ago: The gravitational field is constructed as a physical field in the spirit of Faraday and Maxwell, and … more →
Architectural Cyborgs – Nanotechnology and the Potential for Living Architecture
wrote 1 year ago: The real destiny of the machine [is] to merge itself with natural organisms. - Jack Burnham, B … more →
Can we travel through time?
wrote 1 year ago: Growing up I used to think a lot about time travel. It was both a mental escape and a complete fasci … more →
Domes, Films and Toys: The Role of Education in the Works of Bucky Fuller and Charles and Ray Eames
wrote 1 year ago: In Architecture or Techno-utopia: Politics After Modernism, Felicity Scott maps the migration of mi … more →
Orbitele stabile ale gaurilor negre super-masive ar putea sa aiba propriile lor sisteme planetare
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wrote 1 year ago: Este perfect logic, si, pe deasupra, potrivit ultimelor descoperiri si speculatii astrofizice, chia … more →
Buckminster Fuller, Mixed Metaphors and the Radiolarian
wrote 1 year ago: With the introduction of “Buckyballs” and “Fullerenes” into the scientific lexicon in 1985, Fuller’s … more →
points and geodesics in the pseudosphere
wrote 2 years ago: … more →
Riemann, Langevin & Hamilton [reply]
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wrote 2 years ago: Here is a (prompt!) reply from Mark Girolami corresponding to the earlier post: In preparation for t … more →
Towards Cartan's fixed point theorem: Cosine inequalities and derivative of the distance
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wrote 3 years ago: I am now aiming to prove an important fixed point theorem: Theorem 1 (Elie Cartan) Let be a c … more →
The second variation formula
wrote 3 years ago: I’m going to keep the same notation as before. In particular, we’re studying how the en … more →
Hopf-Rinow II and an application
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wrote 3 years ago: Now, let’s finish the proof of the Hopf-Rinow theorem (the first one) started yesterday. We ne … more →
The Hopf-Rinow theorems and geodesic completeness
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wrote 3 years ago: Ok, yesterday I covered the basic fact that given a Riemannian manifold , the geodesics on (with res … more →
Geodesics are locally length-minimizing
wrote 3 years ago: Fix a Riemannian manifold with metric and Levi-Civita connection . Then we can talk about geodesics … more →
