|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
19 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
2D Riemann-Christoffel curvature tensor via a 3D space using a specialized permutation scheme | | Mensur Omerbashich
; | | Date: |
11 Oct 2009 | | Abstract: | When a space in which Christoffel symbols of the second kind are symmetrical
in lower indices exists, it makes for a supplement to the standard procedure
when a 2D surface is normally induced from the geometry of the surrounding 3D
space in which the surface is embedded. There it appears appropriate to use a
scheme for straightforward permutation of indices of Gkij, when such a space
would make this transformation possible, so as to obtain the components of the
2D Riemann-Christoffel tensor (here expressed in geodetic coordinates for an
ellipsoid of revolution, of use in geophysics). By applying my scheme I find
the corresponding indices in 2D and 3D supplement-spaces, and I compute
components of the Riemann-Christoffel tensor. By operating over the elements of
the projections alone, the all-known value of 1/MN for the Gaussian curvature
on an ellipsoid of revolution is obtained. To further validate my scheme, I
show that in such a 3D space the tangent vector to a PHI-curve for LAM=const1
would be parallel to a tangent vector to a PHI-curve for LAM=const2 on the
surface of an ellipsoid of revolution. Surfaces parameterized by Gauss surface
normal coordinates, such as the Earth, now can have the Riemann-Christopher
curvature tensor computed in a straightforward fashion for the topographic
surface hel(PHIel, LAMel) of the Earth, given Christoffel symbols for such a
representation in terms of orthonormal functions on the ellipsoid of
revolution. | | Source: | arXiv, 0910.1960 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER