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Dergiler / Manas Journal of Engineering / 2022 / Cilt: 10 - Sayı: 1

Generalized fermi derivative on the hypersurfaces

Ayşenur UÇAR
Fatma KARAKUŞ
Sayfa
110–115
Yayın Tarihi
2022-06-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Generalizations have been made in Eⁿ.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı:Generalizations have been made in Eⁿ.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:generalized Fermi derivative · generalized Fermi parallelism · generalized non-rotating frame

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.

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Bu Makaleye Atıf Yap

UÇAR, A., KARAKUŞ, F. (2022). Generalized fermi derivative on the hypersurfaces. Manas Journal of Engineering, Cilt: 10 - Sayı: 1, 110–115. https://ajindex.com/articles/687218

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Kaynakça (19)

  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., Relativ