Open Access
2017 On Complex Homogeneous Space of Vectors with Constraints
Emilija Celakoska, Elena Hadzieva, Vesna Celakoska-Jordanova
J. Geom. Symmetry Phys. 44: 1-11 (2017). DOI: 10.7546/jgsp-44-2017-1-11


A homogeneous space $\mathcal{V}$ of complex constrained vectors in $\mathbb{C}^3,$ representing complex velocities is introduced. The corresponding representation of the complex special orthogonal group of transformations acting on $\mathcal{V}$ is also examined. The requirement for real vector magnitudes is addressed by imposing orthogonality between the real and the imaginary parts of vectors and use of the non-conjugate scalar product. We present the orthogonal transformations acting on $\mathcal{V}$ in terms of the polar decomposition of complex orthogonal matrices. The group link problem and the homogeneity of the space $\mathcal{V}$ are also discussed. Finally, we briefly consider the convenience of the space $\mathcal{V}$ in theoretical calculations.


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Emilija Celakoska. Elena Hadzieva. Vesna Celakoska-Jordanova. "On Complex Homogeneous Space of Vectors with Constraints." J. Geom. Symmetry Phys. 44 1 - 11, 2017.


Published: 2017
First available in Project Euclid: 6 July 2017

zbMATH: 1381.32010
MathSciNet: MR3700453
Digital Object Identifier: 10.7546/jgsp-44-2017-1-11

Rights: Copyright © 2017 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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