SCREEN SEMI INVARIANT LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS

Erol Kılıç; Bayram Şahin; Sadık Keleş

Research Article

Year 2011, Volume: 4 Issue: 2, 120 - 135, 30.10.2011

Erol Kılıç Bayram Şahin Sadık Keleş

Abstract

References

[1] Atçeken, M. and Kılıç, E., Semi-Invariant Lightlike Submanifolds of a Semi-Riemannian Product Manifold, Kodai Math. J. Vol.30, No.3, 361-378, (2007).
[2] Bejan, C.L., 2-Codimensional Lightlike Submanifolds of Almost Para-Hermitian Manifolds, Diﬀerential Geometry and Applications, (1996), 7-17.
[3] Duggal, K.L. and Şahin, B., Screen Cauchy Riemann Ligtlike Submanifolds, Acta Math. Hungar. 106 (1-2), (2005), 137-165.
[4] Duggal, K.L. and Şahin, B., Diﬀerential Geometry of Lightlike Submanifolds, Birkhauser Veralag AG, Basel, Boston, Berlin (2010).
[5] Duggal, K.L., Warped Product of Lightlike Submanifolds, Nonlinear Analysis, 47, (2001), 3061-3072.
[6] Duggal, K.L., Constant Scalar Curvature and Warped Product Globally Null Manifolds, J. Geom. Phys., 43 (2002), 327-340.
[7] Duggal, K.L., and Jin, D.H., Totally Umbilical Lightlike Submanifolds, Kodai Math. J., 26, (2003), 49-68.
[8] Duggal, K.L. and Bejancu, A. Lightlike Submanifolds of Semi-Riemannian Manifolds and Its Applications, Kluwer,Dortrecht, (1996).
[9] Kilic, E. and Şahin, B., Radical Anti-Invariant Lightlike Submanifolds of Semi-Riemannian Product Manifolds, Turk. J. Math. 32, (2008), 429-449.
[10] O’Neill, B., Semi-Riemannian Geometry with Applicitaions to Relativity, Academic Press. New York, (1983).
[11] Şahin, B. and At¸ceken, M., Semi-Invariant Submanifolds of Riemannian Product Manifold. Balkan Journal of Geometry and Its Applications, 8, No:1, (2003), 91-100.
[12] Senlin, X. and Yilong, N., Submanifolds of Product Riemannian Manifold. Acta Mathematica Scientia, 20(B), (2000), 213-218.
[13] Ximin,L. and Shao, F.-M., Skew Semi-Invariant Submanifolds of a Locally Product Manifold. Portugalia Math., Vol.56, Fasc.3, (1999), 319-327.
[14] Yano, K., and Kon, M., Structure on Manifolds. World Scientific Publishing Co.Ltd (1984).

SCREEN SEMI INVARIANT LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS

Year 2011, Volume: 4 Issue: 2, 120 - 135, 30.10.2011

Erol Kılıç Bayram Şahin Sadık Keleş

Abstract

Keywords

Degenerate Metric, Lightlike Submanifold, SCR-Lightlike Submanifold, Product Manifold

References

[1] Atçeken, M. and Kılıç, E., Semi-Invariant Lightlike Submanifolds of a Semi-Riemannian Product Manifold, Kodai Math. J. Vol.30, No.3, 361-378, (2007).
[2] Bejan, C.L., 2-Codimensional Lightlike Submanifolds of Almost Para-Hermitian Manifolds, Diﬀerential Geometry and Applications, (1996), 7-17.
[3] Duggal, K.L. and Şahin, B., Screen Cauchy Riemann Ligtlike Submanifolds, Acta Math. Hungar. 106 (1-2), (2005), 137-165.
[4] Duggal, K.L. and Şahin, B., Diﬀerential Geometry of Lightlike Submanifolds, Birkhauser Veralag AG, Basel, Boston, Berlin (2010).
[5] Duggal, K.L., Warped Product of Lightlike Submanifolds, Nonlinear Analysis, 47, (2001), 3061-3072.
[6] Duggal, K.L., Constant Scalar Curvature and Warped Product Globally Null Manifolds, J. Geom. Phys., 43 (2002), 327-340.
[7] Duggal, K.L., and Jin, D.H., Totally Umbilical Lightlike Submanifolds, Kodai Math. J., 26, (2003), 49-68.
[8] Duggal, K.L. and Bejancu, A. Lightlike Submanifolds of Semi-Riemannian Manifolds and Its Applications, Kluwer,Dortrecht, (1996).
[9] Kilic, E. and Şahin, B., Radical Anti-Invariant Lightlike Submanifolds of Semi-Riemannian Product Manifolds, Turk. J. Math. 32, (2008), 429-449.
[10] O’Neill, B., Semi-Riemannian Geometry with Applicitaions to Relativity, Academic Press. New York, (1983).
[11] Şahin, B. and At¸ceken, M., Semi-Invariant Submanifolds of Riemannian Product Manifold. Balkan Journal of Geometry and Its Applications, 8, No:1, (2003), 91-100.
[12] Senlin, X. and Yilong, N., Submanifolds of Product Riemannian Manifold. Acta Mathematica Scientia, 20(B), (2000), 213-218.
[13] Ximin,L. and Shao, F.-M., Skew Semi-Invariant Submanifolds of a Locally Product Manifold. Portugalia Math., Vol.56, Fasc.3, (1999), 319-327.
[14] Yano, K., and Kon, M., Structure on Manifolds. World Scientific Publishing Co.Ltd (1984).

There are 14 citations in total.

Details

Primary Language	English
Journal Section	Research Article
Authors	Erol Kılıç This is me Bayram Şahin This is me Sadık Keleş This is me
Publication Date	October 30, 2011
Published in Issue	Year 2011 Volume: 4 Issue: 2

Cite

APA	Kılıç, E., Şahin, B., & Keleş, S. (2011). SCREEN SEMI INVARIANT LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS. International Electronic Journal of Geometry, 4(2), 120-135.
AMA	Kılıç E, Şahin B, Keleş S. SCREEN SEMI INVARIANT LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS. Int. Electron. J. Geom. October 2011;4(2):120-135.
Chicago	Kılıç, Erol, Bayram Şahin, and Sadık Keleş. “SCREEN SEMI INVARIANT LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS”. International Electronic Journal of Geometry 4, no. 2 (October 2011): 120-35.
EndNote	Kılıç E, Şahin B, Keleş S (October 1, 2011) SCREEN SEMI INVARIANT LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS. International Electronic Journal of Geometry 4 2 120–135.
IEEE	E. Kılıç, B. Şahin, and S. Keleş, “SCREEN SEMI INVARIANT LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS”, Int. Electron. J. Geom., vol. 4, no. 2, pp. 120–135, 2011.
ISNAD	Kılıç, Erol et al. “SCREEN SEMI INVARIANT LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS”. International Electronic Journal of Geometry 4/2 (October 2011), 120-135.
JAMA	Kılıç E, Şahin B, Keleş S. SCREEN SEMI INVARIANT LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS. Int. Electron. J. Geom. 2011;4:120–135.
MLA	Kılıç, Erol et al. “SCREEN SEMI INVARIANT LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS”. International Electronic Journal of Geometry, vol. 4, no. 2, 2011, pp. 120-35.
Vancouver	Kılıç E, Şahin B, Keleş S. SCREEN SEMI INVARIANT LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN PRODUCT MANIFOLDS. Int. Electron. J. Geom. 2011;4(2):120-35.