Summary
Electromagnetic tensor field can be divided into three classes according as (i) its eigen values are all different (ii) two of its eigen values vanish (iii) all the eigen values vanish. In the first two classes a non-holonomic frame can be constructed from its eigen-vectors and their inverses. Hlavatý (1958) showed using Line-Geometry that a non-holonomic frame can be constructed even in the third class, though in this case, only one vector is an eigen-vector. The purpose of this paper is to obtain all the metrically different frames without using Line-geometry.
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References
Hlavatý, V. (1958):Geometry of Einstein’s Unified Field Theory, P. Noordhoff, Groningen.
Hlavatý, V. (1961):Einstein Maxwell Fields, Journ. de Math., tome XI, Fasc. 1, M. 1–39.
Hlavatý, V. (1961):Einstein Maxwell Fields in the presence of matter and pressure, Annali di Matematica pura ed applicata (IV), Vol. LIII, pp. 21–40.
Mishra, R. S. (1958):Einstein’s connections II. Nondegenerate case, Jour. Math. and Mechanics, 7 (6), pp. 867–892.
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Dedicated to Prof. V. Hlavatý on his 70th. birthday.
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Mishra, R.S. Geometry of Electromagnetic null field. Rend. Circ. Mat. Palermo 12, 155–171 (1963). https://doi.org/10.1007/BF02843962
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DOI: https://doi.org/10.1007/BF02843962