Non-degenerate hypersurfaces of a semi-Riemannian manifold with a semi-symmetric metric connection

Ahmet Yücesan; Nihat Ayyildiz

Archivum Mathematicum (2008)

  • Volume: 044, Issue: 1, page 77-88
  • ISSN: 0044-8753

Abstract

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We derive the equations of Gauss and Weingarten for a non-degenerate hypersurface of a semi-Riemannian manifold admitting a semi-symmetric metric connection, and give some corollaries of these equations. In addition, we obtain the equations of Gauss curvature and Codazzi-Mainardi for this non-degenerate hypersurface and give a relation between the Ricci and the scalar curvatures of a semi-Riemannian manifold and of its a non-degenerate hypersurface with respect to a semi-symmetric metric connection. Eventually, we establish conformal equations of Gauss curvature and Codazzi-Mainardi.

How to cite

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Yücesan, Ahmet, and Ayyildiz, Nihat. "Non-degenerate hypersurfaces of a semi-Riemannian manifold with a semi-symmetric metric connection." Archivum Mathematicum 044.1 (2008): 77-88. <http://eudml.org/doc/250442>.

@article{Yücesan2008,
abstract = {We derive the equations of Gauss and Weingarten for a non-degenerate hypersurface of a semi-Riemannian manifold admitting a semi-symmetric metric connection, and give some corollaries of these equations. In addition, we obtain the equations of Gauss curvature and Codazzi-Mainardi for this non-degenerate hypersurface and give a relation between the Ricci and the scalar curvatures of a semi-Riemannian manifold and of its a non-degenerate hypersurface with respect to a semi-symmetric metric connection. Eventually, we establish conformal equations of Gauss curvature and Codazzi-Mainardi.},
author = {Yücesan, Ahmet, Ayyildiz, Nihat},
journal = {Archivum Mathematicum},
keywords = {semi-symmetric metric connection; Levi-Civita connection; mean curvature; Ricci tensor; conformally flat; semi-symmetric metric connection; Levi-Civita connection; mean curvature; Ricci tensor; conformally flat},
language = {eng},
number = {1},
pages = {77-88},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Non-degenerate hypersurfaces of a semi-Riemannian manifold with a semi-symmetric metric connection},
url = {http://eudml.org/doc/250442},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Yücesan, Ahmet
AU - Ayyildiz, Nihat
TI - Non-degenerate hypersurfaces of a semi-Riemannian manifold with a semi-symmetric metric connection
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 1
SP - 77
EP - 88
AB - We derive the equations of Gauss and Weingarten for a non-degenerate hypersurface of a semi-Riemannian manifold admitting a semi-symmetric metric connection, and give some corollaries of these equations. In addition, we obtain the equations of Gauss curvature and Codazzi-Mainardi for this non-degenerate hypersurface and give a relation between the Ricci and the scalar curvatures of a semi-Riemannian manifold and of its a non-degenerate hypersurface with respect to a semi-symmetric metric connection. Eventually, we establish conformal equations of Gauss curvature and Codazzi-Mainardi.
LA - eng
KW - semi-symmetric metric connection; Levi-Civita connection; mean curvature; Ricci tensor; conformally flat; semi-symmetric metric connection; Levi-Civita connection; mean curvature; Ricci tensor; conformally flat
UR - http://eudml.org/doc/250442
ER -

References

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  4. Friedmann, A., Schouten, J. A., 10.1007/BF01187468, Math. Z. 21 (1924), 211–223. (1924) MR1544701DOI10.1007/BF01187468
  5. Hayden, H. A., Subspace of a space with torsion, Proc. London Math. Soc. 34 (1932), 27–50. (1932) 
  6. Imai, T., Hypersurfaces of a Riemannian manifold with semi-symmetric metric connection, Tensor (N.S.) 23 (1972), 300–306. (1972) Zbl0262.53041MR0336597
  7. Imai, T., Notes on semi-symmetric metric connections, Tensor (N.S.) 24 (1972), 293–296. (1972) Zbl0251.53038MR0375121
  8. Konar, A., Biswas, B., Lorentzian manifold that admits a type of semi-symmetric metric connection, Bull. Calcutta Math. Soc. 93 (5) (2001), 427–437. (2001) Zbl1021.53043MR1909170
  9. O’Neill, B., Semi-Riemannian geometry with applications to relativity, Academic Press, London, 1983. (1983) MR0719023
  10. Yano, K., On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl. 15 (1970), 1579–1586. (1970) Zbl0213.48401MR0275321

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