Connection Forms of an Orthonormal Frame Field in the Minkowski Space
Pure and Applied Mathematics Journal
Volume 4, Issue 1-2, January 2015, Pages: 10-13
Received: Oct. 13, 2014;
Accepted: Nov. 10, 2014;
Published: Jan. 12, 2015
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Keziban Orbay, Amasya University, Faculty of Education, Amasya, Turkey
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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.
Minkowski Space, One-Form, Connection Forms
To cite this article
Connection Forms of an Orthonormal Frame Field in the Minkowski Space, Pure and Applied Mathematics Journal. Special Issue: Applications of Geometry.
Vol. 4, No. 1-2,
2015, pp. 10-13.
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.
Darling RWR. Differential Forms and Connections, Cambridge University Press, 1994.
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.
Morita, S., Nagase, T. and Nomizu, K. Geometry of Differential Forms (Translations of Mathematical Monoqraphs, Vol.201). Amer. Math. Soc., 2001.
O’Neill, B. Semi-Riemannian Geometry with Applications to Relativity. Academic Press, 1983.
O’Neill, B. Elementary Differential Geometry, Revised Second Edition, Academic Press, 2006.
Waner, S. Introduction to Differential Geometry and General Relativity, Hofstra University, 2005.
Woestijne, V.D.I. Minimal Surfaces in the 3-dimensional Minkowski Space, World Scientific Press. Singapore, 1990.