## Journal of Geometry and Symmetry in Physics

### On Complex Homogeneous Space of Vectors with Constraints

#### Abstract

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.

#### Article information

Source
J. Geom. Symmetry Phys., Volume 44 (2017), 1-11.

Dates
First available in Project Euclid: 6 July 2017

https://projecteuclid.org/euclid.jgsp/1499306418

Digital Object Identifier
doi:10.7546/jgsp-44-2017-1-11

Mathematical Reviews number (MathSciNet)
MR3700453

Zentralblatt MATH identifier
1381.32010

#### Citation

Celakoska, Emilija; Hadzieva, Elena; Celakoska-Jordanova, Vesna. On Complex Homogeneous Space of Vectors with Constraints. J. Geom. Symmetry Phys. 44 (2017), 1--11. doi:10.7546/jgsp-44-2017-1-11. https://projecteuclid.org/euclid.jgsp/1499306418