In this work, connection formulas and forms of an orthonormal frame field in the Minkowski space were introduced and then the variation of connection forms was studied. In addition, the relation between the matrix of connection forms and the transition matrix of an orthonormal basis of tangent space were established, and an example was illustrated.
| Published in |
Pure and Applied Mathematics Journal (Volume 4, Issue 1-2)
This article belongs to the Special Issue Applications of Geometry |
| DOI | 10.11648/j.pamj.s.2015040102.13 |
| Page(s) | 10-13 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2015. Published by Science Publishing Group |
Minkowski Space, One-Form, Connection Forms
| [1] | Akutagawa, K. and Nishikawa S. The Gauss Map and Space-like Surfaces with Prescribed Mean Curvature in Minkowski 3-space. Tohoku Math. J., 42(2) ,1990. |
| [2] | Darling RWR. Differential Forms and Connections, Cambridge University Press, 1994. |
| [3] | Kalimuthu, S. A Brief History of the Fifth Euclidean Postulate and Two New Results. The General Sci. J., 2009, www.wbabin.net/physics/kalimuthu9.pdf. |
| [4] | Morita, S., Nagase, T. and Nomizu, K. Geometry of Differential Forms (Translations of Mathematical Monoqraphs, Vol.201). Amer. Math. Soc., 2001. |
| [5] | O’Neill, B. Semi-Riemannian Geometry with Applications to Relativity. Academic Press, 1983. |
| [6] | O’Neill, B. Elementary Differential Geometry, Revised Second Edition, Academic Press, 2006. |
| [7] | Waner, S. Introduction to Differential Geometry and General Relativity, Hofstra University, 2005. |
| [8] | Woestijne, V.D.I. Minimal Surfaces in the 3-dimensional Minkowski Space, World Scientific Press. Singapore, 1990. |
APA Style
Keziban Orbay. (2015). Connection Forms of an Orthonormal Frame Field in the Minkowski Space. Pure and Applied Mathematics Journal, 4(1-2), 10-13. https://doi.org/10.11648/j.pamj.s.2015040102.13
ACS Style
Keziban Orbay. Connection Forms of an Orthonormal Frame Field in the Minkowski Space. Pure Appl. Math. J. 2015, 4(1-2), 10-13. doi: 10.11648/j.pamj.s.2015040102.13
AMA Style
Keziban Orbay. Connection Forms of an Orthonormal Frame Field in the Minkowski Space. Pure Appl Math J. 2015;4(1-2):10-13. doi: 10.11648/j.pamj.s.2015040102.13
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Download@article{10.11648/j.pamj.s.2015040102.13,
author = {Keziban Orbay},
title = {Connection Forms of an Orthonormal Frame Field in the Minkowski Space},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {1-2},
pages = {10-13},
doi = {10.11648/j.pamj.s.2015040102.13},
url = {https://doi.org/10.11648/j.pamj.s.2015040102.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040102.13},
abstract = {In this work, connection formulas and forms of an orthonormal frame field in the Minkowski space were introduced and then the variation of connection forms was studied. In addition, the relation between the matrix of connection forms and the transition matrix of an orthonormal basis of tangent space were established, and an example was illustrated.},
year = {2015}
}
TY - JOUR T1 - Connection Forms of an Orthonormal Frame Field in the Minkowski Space AU - Keziban Orbay Y1 - 2015/01/12 PY - 2015 N1 - https://doi.org/10.11648/j.pamj.s.2015040102.13 DO - 10.11648/j.pamj.s.2015040102.13 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 10 EP - 13 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2015040102.13 AB - In this work, connection formulas and forms of an orthonormal frame field in the Minkowski space were introduced and then the variation of connection forms was studied. In addition, the relation between the matrix of connection forms and the transition matrix of an orthonormal basis of tangent space were established, and an example was illustrated. VL - 4 IS - 1-2 ER -
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