Vol. 2 No. 14 (2025): International Journal of Science and Technology
Articles

ON COMPLEX HYPERPLANES IN Cn SPACE AND THEIR PROJECTIONS IN REAL SPACE

Published 04-11-2025

Keywords

  • real space, complex space, real plane, complex hyperplane

How to Cite

ON COMPLEX HYPERPLANES IN Cn SPACE AND THEIR PROJECTIONS IN REAL SPACE. (2025). INTERNATIONAL JOURNAL OF SCIENCE AND TECHNOLOGY, 2(14), 31-34. https://doi.org/10.70728/tech.v02.i14.007

Abstract

This article studies the projections of complex hyperplanes in the real space of Cn. In particular, it proves
a theorem stating that for any m ≤ n dimensional real plane taken from the space Rn ⊂ Cn, there exists a
unique m-dimensional complex plane that contains it.

References

  1. 1. B.V. Shabat. Introduction to complex Analysis
  2. Part II Functions of Several variables. American
  3. Mathematical Society, (1992) 1-12.
  4. 2. Rudin W., Principles of Mathematical Analysis,
  5. R.R. Donnelley & Sons, 1976, pp. 16–19.
  6. 3. Drnovsek, B.D., Forstnerich F.: Minimal hulls of
  7. compact sets in .. Trans. Am. Math. Soc. 368(10),
  8. 7477–7506, October 2016.
  9. 4. Harvey F. R. and Lawson H. B. Jr., An
  10. introduction to potential theory in calibrated
  11. geometry. Amer. J. Math., V. 131, no. 4, (2009),
  12. 893-944.
  13. 5. Harvey F. R. and Lawson H. B. Jr., Duality
  14. of positive currents and plurisubharmonic
  15. functions in calibrated geometry. Amer. J.
  16. Math.,V. 131, no. 5, (2009), 1211-1240.
  17. 6. Harvey F. R. and Lawson H. B. Jr., Geometric
  18. plurisubharmonicity and convexity – an
  19. introduction. Advances in Mathematics, V. 230,
  20. (2012), 2428-2456.
  21. 7. Harvey F. R. and Lawson H. B. Jr.,
  22. Plurisubharmonicity in a general geometric
  23. context. Geometry and Analysis I, (2010),
  24. 363-401.
  25. 8. Harvey F.R. and Lawson H. B. Jr., Calibrated
  26. geometries // Acta Mathematica 148, 1982, pp.
  27. 47-157.
  28. 9. Harvey F.R. and Lawson H.B.Jr., convexity,
  29. plurisubharmonicity and the Levi problem//
  30. Indiana Univ. Math. J. 62 no. 1 (2013), 149-169.
  31. 10. Joyce D., Riemannian holonomy groups and
  32. calibrated geometry. Oxford University Press, –
  33. U.S.A. 2007. – 318 p.