Research Article
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Year 2022, Volume: 10 Issue: 1, 110 - 115, 30.06.2022
https://doi.org/10.51354/mjen.937100

Abstract

References

  • [1] Balakrishnan R., "Space curves, anholonomy and nonlinearity," Pramana Journal of Physics., 64(4), 2005, 607-615.
  • [2] Benn I.M. and Tucker R.W., "Wave mechanics and inertial guidance," Bull. The American Physical Society, 39(6), (1989), 1594-1601.
  • [3] Berry M.V., "Quantal phase factors accompanying adiabatic changes," Proc. R. Soc. London A 392, (1984).
  • [4] Dandolo¤ R., "Berrys phase and Fermi-Walker parallel transport," Elsevier Science Publish- ers, 139(1-2), (1989), 19-20.
  • [5] Fermi E., Atti Accad. Naz. Lincei Cl. Sci. Fiz. Mat. Nat., 31 (1922) 184-306.
  • [6] H. W. Guggenheimer, Di¤erential Geometry. McGraw-Hill, New York, 1963.
  • [7] Hawking S.W. and Ellis G. F. R., The Large Scale Structure of Spacetime. Cambridge Univ. Press, 1973.
  • [8] Hehl F.W., Lemke J., and Mielke E.W., "Two lectures on Fermions and Gravity," Geometry and Theoretical Physics. J. Debrus and A.C. Hirshfeld (eds.), Springer Verlag, N.Y., (1991), 56- 140.
  • [9] Karaku¸s F. and Yaylı., "On the Fermi-Walker derivative and non-rotating frame," Int. Journal of Geometric Methods in Modern Physics, 9(8), (2012), 1250066(11 pp.).
  • [10] Karaku¸s F. and Yaylı., "The Fermi derivative in the hypersurfaces," Int. Journal of Geo- metric Methods in Modern Physics, 12, (2015), 1550002 (12 pp.).
  • [11] Manoff S., "Fermi derivative and Fermi-Walker transports over (Ln;g) spaces," Internat. J. Modern Phys. A, 13(25), (1998), 4289-4308.
  • [12] O'Neill B., Elementary Di¤erential Geometry. Academic Press, New York, 1966.
  • [13] Pripoae G. T., "Generalized Fermi-Walker transport," LibertasMath., XIX, 1999, 65-69.
  • [14] Pripoae G. T., "Generalized Fermi-Walker parallelism induced by generalized Schouthen connections," in Proceedings of the Conference of Applied Di¤erential Geometry-General Relativity and the Workshop on Global Analysis Balkan Society of Geometers. Di¤erential Geometry and Lie Algebras, Balkan Society of Geometers, 2000, 117-125.
  • [15] Sachs R. K. and Wu H., General Relativity for Mathematicians. Springer Verlag, N.Y., 1977.
  • [16] Thorpe J. A., Elementary Topics in Di¤erential Geometry. SpringerVerlag, Berlin, 1979, pp. 45-52.
  • [17] Uçar A., Karaku¸s F., and Yaylı., "Generalized Fermi-Walker derivative and non-rotating frame," Int. Journal of Geometric Methods in Modern Physics, 14(09), (2017), 1750131- 1750141, Doi: 10.1142/S0219887817501316.
  • [18] Uçar, A. "Genelle¸stirilmi¸s Fermi-Walker türevi ve geometrik uygulamalar¬," Ph. D. thesis, Sinop University, Sinop, Turkey, (2019).
  • [19] Walker A. G., Relative co-ordinates. Proc. Royal Soc. Edinburgh, 52 (1932) 345-353.
  • [20] Weinberg S., Gravitation and Cosmology. J. Wiley Publ., N.Y, 1972.

Generalized fermi derivative on the hypersurfaces

Year 2022, Volume: 10 Issue: 1, 110 - 115, 30.06.2022
https://doi.org/10.51354/mjen.937100

Abstract

In this paper, generalized Fermi derivative, generalized Fermi parallelism, and generalized non-rotating frame concepts are given along any curve on any hypersurface in Eⁿ⁺¹ Euclidean space. The generalized Fermi derivative of a vector field and being generalized non-rotating conditions are analyzed along the curve on the surface in Euclidean 3-space. Then a correlation is found between generalized Fermi derivative, Fermi derivative, and Levi-Civita derivative in E³. Then we examine generalized Fermi parallel vector fields and conditions of being generalized non-rotating frame with the tensor field in E⁴. Generalizations have been made in Eⁿ.

References

  • [1] Balakrishnan R., "Space curves, anholonomy and nonlinearity," Pramana Journal of Physics., 64(4), 2005, 607-615.
  • [2] Benn I.M. and Tucker R.W., "Wave mechanics and inertial guidance," Bull. The American Physical Society, 39(6), (1989), 1594-1601.
  • [3] Berry M.V., "Quantal phase factors accompanying adiabatic changes," Proc. R. Soc. London A 392, (1984).
  • [4] Dandolo¤ R., "Berrys phase and Fermi-Walker parallel transport," Elsevier Science Publish- ers, 139(1-2), (1989), 19-20.
  • [5] Fermi E., Atti Accad. Naz. Lincei Cl. Sci. Fiz. Mat. Nat., 31 (1922) 184-306.
  • [6] H. W. Guggenheimer, Di¤erential Geometry. McGraw-Hill, New York, 1963.
  • [7] Hawking S.W. and Ellis G. F. R., The Large Scale Structure of Spacetime. Cambridge Univ. Press, 1973.
  • [8] Hehl F.W., Lemke J., and Mielke E.W., "Two lectures on Fermions and Gravity," Geometry and Theoretical Physics. J. Debrus and A.C. Hirshfeld (eds.), Springer Verlag, N.Y., (1991), 56- 140.
  • [9] Karaku¸s F. and Yaylı., "On the Fermi-Walker derivative and non-rotating frame," Int. Journal of Geometric Methods in Modern Physics, 9(8), (2012), 1250066(11 pp.).
  • [10] Karaku¸s F. and Yaylı., "The Fermi derivative in the hypersurfaces," Int. Journal of Geo- metric Methods in Modern Physics, 12, (2015), 1550002 (12 pp.).
  • [11] Manoff S., "Fermi derivative and Fermi-Walker transports over (Ln;g) spaces," Internat. J. Modern Phys. A, 13(25), (1998), 4289-4308.
  • [12] O'Neill B., Elementary Di¤erential Geometry. Academic Press, New York, 1966.
  • [13] Pripoae G. T., "Generalized Fermi-Walker transport," LibertasMath., XIX, 1999, 65-69.
  • [14] Pripoae G. T., "Generalized Fermi-Walker parallelism induced by generalized Schouthen connections," in Proceedings of the Conference of Applied Di¤erential Geometry-General Relativity and the Workshop on Global Analysis Balkan Society of Geometers. Di¤erential Geometry and Lie Algebras, Balkan Society of Geometers, 2000, 117-125.
  • [15] Sachs R. K. and Wu H., General Relativity for Mathematicians. Springer Verlag, N.Y., 1977.
  • [16] Thorpe J. A., Elementary Topics in Di¤erential Geometry. SpringerVerlag, Berlin, 1979, pp. 45-52.
  • [17] Uçar A., Karaku¸s F., and Yaylı., "Generalized Fermi-Walker derivative and non-rotating frame," Int. Journal of Geometric Methods in Modern Physics, 14(09), (2017), 1750131- 1750141, Doi: 10.1142/S0219887817501316.
  • [18] Uçar, A. "Genelle¸stirilmi¸s Fermi-Walker türevi ve geometrik uygulamalar¬," Ph. D. thesis, Sinop University, Sinop, Turkey, (2019).
  • [19] Walker A. G., Relative co-ordinates. Proc. Royal Soc. Edinburgh, 52 (1932) 345-353.
  • [20] Weinberg S., Gravitation and Cosmology. J. Wiley Publ., N.Y, 1972.
There are 20 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Ayşenur Uçar 0000-0002-7498-6752

Fatma Karakuş 0000-0003-0379-4232

Early Pub Date July 3, 2022
Publication Date June 30, 2022
Published in Issue Year 2022 Volume: 10 Issue: 1

Cite

APA Uçar, A., & Karakuş, F. (2022). Generalized fermi derivative on the hypersurfaces. MANAS Journal of Engineering, 10(1), 110-115. https://doi.org/10.51354/mjen.937100
AMA Uçar A, Karakuş F. Generalized fermi derivative on the hypersurfaces. MJEN. June 2022;10(1):110-115. doi:10.51354/mjen.937100
Chicago Uçar, Ayşenur, and Fatma Karakuş. “Generalized Fermi Derivative on the Hypersurfaces”. MANAS Journal of Engineering 10, no. 1 (June 2022): 110-15. https://doi.org/10.51354/mjen.937100.
EndNote Uçar A, Karakuş F (June 1, 2022) Generalized fermi derivative on the hypersurfaces. MANAS Journal of Engineering 10 1 110–115.
IEEE A. Uçar and F. Karakuş, “Generalized fermi derivative on the hypersurfaces”, MJEN, vol. 10, no. 1, pp. 110–115, 2022, doi: 10.51354/mjen.937100.
ISNAD Uçar, Ayşenur - Karakuş, Fatma. “Generalized Fermi Derivative on the Hypersurfaces”. MANAS Journal of Engineering 10/1 (June 2022), 110-115. https://doi.org/10.51354/mjen.937100.
JAMA Uçar A, Karakuş F. Generalized fermi derivative on the hypersurfaces. MJEN. 2022;10:110–115.
MLA Uçar, Ayşenur and Fatma Karakuş. “Generalized Fermi Derivative on the Hypersurfaces”. MANAS Journal of Engineering, vol. 10, no. 1, 2022, pp. 110-5, doi:10.51354/mjen.937100.
Vancouver Uçar A, Karakuş F. Generalized fermi derivative on the hypersurfaces. MJEN. 2022;10(1):110-5.

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