Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematical Physics

arXiv:0712.3067 (math-ph)
[Submitted on 19 Dec 2007 (v1), last revised 4 Dec 2008 (this version, v6)]

Title:Differential Forms on Riemannian (Lorentzian) and Riemann-Cartan Structures and Some Applications to Physics

Authors:Waldyr A. Rodrigues Jr
View PDF
Abstract: In this paper after recalling some essential tools concerning the theory of differential forms in the Cartan, Hodge and Clifford bundles over a Riemannian or Riemann-Cartan space or a Lorentzian or Riemann-Cartan spacetime we solve with details several exercises involving different grades of difficult. One of the problems is to show that a recent formula appearing in the literature for the exterior covariant derivative of the Hodge dual of the torsion 2-forms is simply wrong. We believe that the paper will be useful for students (and eventually for some experts) on applications of differential geometry on physical problems. A detailed account of the issues discussed in the paper appears in the table of contents.
Comments: Some few important misprints appearing in the version of the paper published in AFLB (in a special issue dedicated to torsion) are corrected
Subjects: Mathematical Physics (math-ph)
Cite as: arXiv:0712.3067 [math-ph]
  (or arXiv:0712.3067v6 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.0712.3067
Journal reference: Ann. Fond. L. de Broglie 32 (4), 425-478 (2007)

Submission history

From: Waldyr A. Rodrigues Jr. [view email]
[v1] Wed, 19 Dec 2007 16:32:42 UTC (61 KB)
[v2] Wed, 2 Jan 2008 10:08:09 UTC (62 KB)
[v3] Mon, 7 Jan 2008 16:04:03 UTC (62 KB)
[v4] Mon, 12 May 2008 14:36:40 UTC (62 KB)
[v5] Tue, 20 May 2008 12:28:27 UTC (62 KB)
[v6] Thu, 4 Dec 2008 19:14:04 UTC (62 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math-ph
< prev   |   next >
new | recent | 2007-12
Change to browse by:
math
math.MP

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)