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Year 2013, Volume: 1 Issue: 1, 18 - 35, 01.06.2013

Abstract

❧✐❦❡ ❤②♣❡rs✉❡r❢❛❝❡s✳ ❙❡❝t✐♦♥ ✸ ✐♥tr♦❞✉❝❡s ❛ss♦❝✐❛t❡ ♠❡tr✐❝ t♦ ❛ ♥♦r♠❛❧✐③❡❞ ❧✐❣❤t❧✐❦❡ ❤②♣❡rs✉r❢❛❝❡ t❤r♦✉❣❤ ♣s❡✉❞♦✲✐♥✈❡rs✐♦♥ ♦❢ ❞❡❣❡♥❡r❛t❡ ♠❡tr✐❝s ❛♥❞ s❡❝t✐♦♥ ✹ ❞❡❛❧s ✇✐t❤ t❤❡ ❞❡t❡r♠✐♥❛♥t ♦❢ t❤❡ ❛ss♦❝✐❛t❡ ♠❡tr✐❝ r❡❧❛t✐✈❡ t♦ t❤❡ ✐♥❞✉❝❡❞ ✈♦❧✉♠❡ ❡❧❡♠❡♥t✳ ■♥ s❡❝t✐♦♥ ✺ ✇❡ ♣r❡s❡♥t ❛ t❡❝❤♥✐❝❛❧ ❧❡♠♠❛ ❛❝❝♦✉♥t✐♥❣ ♦♥ ❤♦✇ ✐♥❞✉❝❡❞ ❣❡♦♠❡tr✐❝ ♦❜❥❡❝ts ❝❤❛♥❣❡ ✉♥❞❡r ❝❤❛♥❣❡ ✐♥ ♥♦r♠❛❧✐③❛t✐♦♥ ❢♦❧❧♦✇❡❞ ❜② ❛ ❝♦♠♣❛t✐❜✐❧✐t② r❡s✉❧t ♥❡❡❞❡❞ ✐♥ t❤❡ ❢♦r♠✉❧❛t✐♦♥ ♦❢ ♦✉r ♥♦r♠❛❧✐③❛t✐♦♥ ❝♦♥str❛✐♥ts✳ ❚❤❡r❡❛❢t❡r✱ ✇❡ ❝♦♥s✐❞❡r ✐♥ s❡❝t✐♦♥ ✻ t❤❡ ✐♥✈❛r✐❛♥t ♥♦r♠❛❧✐③✐♥❣ ❞✐✛❡r❡♥t✐❛❧ ❡q✉❛t✐♦♥ ❛♥❞ ✐♥tr♦❞✉❝❡ ✐♥ s❡❝t✐♦♥ ✼ t❤❡ ❝❛❧✐❜r❛t❡❞ ❞✐✈❡r❣❡♥❝❡ ♦❢ s❡❝t✐♦♥s ❛❧♦♥❣ t❤❡ ♥✉❧❧ ❤②♣❡rs✉❡r❢❛❝❡s✳ ❋✐♥❛❧❧②✱ ✇❡ ♣r❡s❡♥t t❤❡ ♠❛✐♥ r❡s✉❧t ✐♥ s❡❝t✐♦♥ ✽ ❢♦❧❧♦✇❡❞ ❜② ❛ ❜❛s✐❝ ❡①❛♠♣❧❡ ♦♥ t❤❡ ♥✉❧❧ ❝♦♥❡ ∧3⊂ R4✳

References

  • Akivis, M. A. and Goldberg, V. V. On Some Methods of Construction of Invariant Normaliza- tions of Lightlike Hypersurfaces. Di . Geom. Appl. 12 (2000), p. 121-143.
  • Akivis, M. A. and Goldberg, V. V. Lightlike Hypersurfaces on Manifolds Endowed with a Con- formal Structur of Lorentzian Signature. Acta Appl. Math. 57 (1999), p.155-185.
  • Atindogbe, C.Normalization and prescribed extrinsic scalar curvature on lightlike hypersurfaces, Journal of Geometry and Physics 60 (2010) 1762–1770.
  • Atindogbe, C. Blaschke type normalization on light-Like Hypersurfaces, Journal of Mathemat- ical Physics, Analysis, Geometry 6 (2010) No. 4, pp. 362-382.
  • Atindogbe, C. Scalar curvature on lightlike hypersurfaces Applied Sciences, Vol.11, 2009, pp. 18.
  • Atindogbe, C. and Ezin, J.-P. and J. Tossa Pseudo-inversion of degenerate metrics Int. J. of Mathematics and Mathematical Sciences, 55 (2003), 3479-3501.
  • Atindogbe, C. and K.L. Duggal, K. L. Conformal screen on lightlike hypersurfaces., Int. J. of Pure and Applied Math., 11 (2004), 421-442.
  • E. Bekkara, C. Frances and A. Zeghib On lightlike geometry: isometric actions and rigidity aspects. C. R. Acad. Sci. Paris, Ser. (2006), 1343, p. 317-321.
  • Carter, B. Killing Horizons and Orthogonally Transitive Groups in Space-time. J. Math. Phys. (1969), 1, p. 70-81.
  • Chrusciel, P. T. Delay, E. and Galloway, G. J. Howard, R. Regularity of the horizon and the Area Theorem, Annales Henri Poincaré, 2001,2, p.109-178. gr-qc/0001003.
  • Duggal, K. L. On scalar curvature in lightlike geometry, J. Geom. Phy., 57 (2007) 473-481.
  • Duggal, K. L. and Bejancu, A. Lightlike submanifolds of semi-Riemannian Manifolds and Ap- plications. Kluwer Acad. Publishers, Dordrecht, Volume 364, 1996.
  • Katsuno, K. Null Hypersurfaces in Lorentzian Manifolds. Math. Proc. Cab. Phil. Soc. 88 (1980), p. 175-182.
  • Kupeli, D. N. Singular Semi-Riemannian Geometry. Kluwer Acad. Publishers, Dordrecht, vol- ume 366, 1996.
  • Larsen, J. C. Singular Semi-Riemannian Geometry. J. Geom. Phys. 9 (1992), No. 1, p. 3-23.
  • Larsen, J. C. Submanifold Geometry. J. Geom. Anal. 4 (1994),No. 2, p. 189-205.
  • Penrose, R. The Twistor Geometry of Light Rays. Geometry and Physics, Clas- sical Quantum Gravity (1997), 14 (1A), p. A299-A323.
  • Pinl, M. Zur Theorie del Halbisotrope Flachen im R4. J. Geom. Phys 1 (1992), 9, p. 3-23.
  • Taub, A. H. Singular Hypersurfaces in General Rrelativity. Illinois J. Math 1 (1957), p.378-388.
  • Institut de Mathématiques et de Sciences Physiques (IMSP), Université d'Abomey- Calavi, 01 BP 613 Porto-Novo, Bénin E-mail address: atincyr@gmail.com, atincyr@imsp-uac.org. Institut Elie Cartan, Université de Lorraine,, B.P. 239 54506 Vandğuvre-lès- Nancy Cedex, France
  • E-mail address: lionel.berard-bergery@univ-lorraine.fr

DISTINGUISHED NORMALIZATION ON NON-MINIMAL NULL HYPERSURFACES

Year 2013, Volume: 1 Issue: 1, 18 - 35, 01.06.2013

Abstract

We show that on a non-minimal lightlike hypersurface with nullity
degree 1, there exists a unique null transversal (normalizing) vector eld with
prescribed calibrated divergence, for which the induced connection and the LeviCivita
connection of the associate non-degenerate metric coincide.

References

  • Akivis, M. A. and Goldberg, V. V. On Some Methods of Construction of Invariant Normaliza- tions of Lightlike Hypersurfaces. Di . Geom. Appl. 12 (2000), p. 121-143.
  • Akivis, M. A. and Goldberg, V. V. Lightlike Hypersurfaces on Manifolds Endowed with a Con- formal Structur of Lorentzian Signature. Acta Appl. Math. 57 (1999), p.155-185.
  • Atindogbe, C.Normalization and prescribed extrinsic scalar curvature on lightlike hypersurfaces, Journal of Geometry and Physics 60 (2010) 1762–1770.
  • Atindogbe, C. Blaschke type normalization on light-Like Hypersurfaces, Journal of Mathemat- ical Physics, Analysis, Geometry 6 (2010) No. 4, pp. 362-382.
  • Atindogbe, C. Scalar curvature on lightlike hypersurfaces Applied Sciences, Vol.11, 2009, pp. 18.
  • Atindogbe, C. and Ezin, J.-P. and J. Tossa Pseudo-inversion of degenerate metrics Int. J. of Mathematics and Mathematical Sciences, 55 (2003), 3479-3501.
  • Atindogbe, C. and K.L. Duggal, K. L. Conformal screen on lightlike hypersurfaces., Int. J. of Pure and Applied Math., 11 (2004), 421-442.
  • E. Bekkara, C. Frances and A. Zeghib On lightlike geometry: isometric actions and rigidity aspects. C. R. Acad. Sci. Paris, Ser. (2006), 1343, p. 317-321.
  • Carter, B. Killing Horizons and Orthogonally Transitive Groups in Space-time. J. Math. Phys. (1969), 1, p. 70-81.
  • Chrusciel, P. T. Delay, E. and Galloway, G. J. Howard, R. Regularity of the horizon and the Area Theorem, Annales Henri Poincaré, 2001,2, p.109-178. gr-qc/0001003.
  • Duggal, K. L. On scalar curvature in lightlike geometry, J. Geom. Phy., 57 (2007) 473-481.
  • Duggal, K. L. and Bejancu, A. Lightlike submanifolds of semi-Riemannian Manifolds and Ap- plications. Kluwer Acad. Publishers, Dordrecht, Volume 364, 1996.
  • Katsuno, K. Null Hypersurfaces in Lorentzian Manifolds. Math. Proc. Cab. Phil. Soc. 88 (1980), p. 175-182.
  • Kupeli, D. N. Singular Semi-Riemannian Geometry. Kluwer Acad. Publishers, Dordrecht, vol- ume 366, 1996.
  • Larsen, J. C. Singular Semi-Riemannian Geometry. J. Geom. Phys. 9 (1992), No. 1, p. 3-23.
  • Larsen, J. C. Submanifold Geometry. J. Geom. Anal. 4 (1994),No. 2, p. 189-205.
  • Penrose, R. The Twistor Geometry of Light Rays. Geometry and Physics, Clas- sical Quantum Gravity (1997), 14 (1A), p. A299-A323.
  • Pinl, M. Zur Theorie del Halbisotrope Flachen im R4. J. Geom. Phys 1 (1992), 9, p. 3-23.
  • Taub, A. H. Singular Hypersurfaces in General Rrelativity. Illinois J. Math 1 (1957), p.378-388.
  • Institut de Mathématiques et de Sciences Physiques (IMSP), Université d'Abomey- Calavi, 01 BP 613 Porto-Novo, Bénin E-mail address: atincyr@gmail.com, atincyr@imsp-uac.org. Institut Elie Cartan, Université de Lorraine,, B.P. 239 54506 Vandğuvre-lès- Nancy Cedex, France
  • E-mail address: lionel.berard-bergery@univ-lorraine.fr
There are 21 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Cyriaque Atındogbe 0000-0001-8346-4027

Lionel Berardbergery This is me

Publication Date June 1, 2013
Submission Date March 9, 2015
Published in Issue Year 2013 Volume: 1 Issue: 1

Cite

APA Atındogbe, C., & Berardbergery, L. (2013). DISTINGUISHED NORMALIZATION ON NON-MINIMAL NULL HYPERSURFACES. Mathematical Sciences and Applications E-Notes, 1(1), 18-35.
AMA Atındogbe C, Berardbergery L. DISTINGUISHED NORMALIZATION ON NON-MINIMAL NULL HYPERSURFACES. Math. Sci. Appl. E-Notes. June 2013;1(1):18-35.
Chicago Atındogbe, Cyriaque, and Lionel Berardbergery. “DISTINGUISHED NORMALIZATION ON NON-MINIMAL NULL HYPERSURFACES”. Mathematical Sciences and Applications E-Notes 1, no. 1 (June 2013): 18-35.
EndNote Atındogbe C, Berardbergery L (June 1, 2013) DISTINGUISHED NORMALIZATION ON NON-MINIMAL NULL HYPERSURFACES. Mathematical Sciences and Applications E-Notes 1 1 18–35.
IEEE C. Atındogbe and L. Berardbergery, “DISTINGUISHED NORMALIZATION ON NON-MINIMAL NULL HYPERSURFACES”, Math. Sci. Appl. E-Notes, vol. 1, no. 1, pp. 18–35, 2013.
ISNAD Atındogbe, Cyriaque - Berardbergery, Lionel. “DISTINGUISHED NORMALIZATION ON NON-MINIMAL NULL HYPERSURFACES”. Mathematical Sciences and Applications E-Notes 1/1 (June 2013), 18-35.
JAMA Atındogbe C, Berardbergery L. DISTINGUISHED NORMALIZATION ON NON-MINIMAL NULL HYPERSURFACES. Math. Sci. Appl. E-Notes. 2013;1:18–35.
MLA Atındogbe, Cyriaque and Lionel Berardbergery. “DISTINGUISHED NORMALIZATION ON NON-MINIMAL NULL HYPERSURFACES”. Mathematical Sciences and Applications E-Notes, vol. 1, no. 1, 2013, pp. 18-35.
Vancouver Atındogbe C, Berardbergery L. DISTINGUISHED NORMALIZATION ON NON-MINIMAL NULL HYPERSURFACES. Math. Sci. Appl. E-Notes. 2013;1(1):18-35.

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