[1] Bejan, C. L., Duggal, K. L., Global lightlike manifolds and harmonicity, Kodai Math. J.,
28(2005), 131-145.
[2] Chen, B.-Y., Some pinching and classification theorems for minimal submanifolds, Arch. Math.
(Brno), 60(1993), 568-578.
[3] Chen, B-Y., Strings of Riemannian invariants, inequalities, ideal immersions and their
applications, in: The Third Pacific Rim Geom. Conf.
Internat Press, Cambridge, MA, (1998), 7-60.
[4] Chen, B.-Y., Riemannian DNA, inequalities and their applications, Tamkang J. of Sci. and Eng.,
3(2000), no.3, 123-130.
[5] Chen, B.-Y., Some new obstructions to minimal and Lagrangian isometric immersions, Japan. J.
Math., 26(2000), 105-127.
[6] Chen, B.-Y., Pseudo-Riemannian geometry, δ-invariants and applications, World Scientific
Publishing, Hackensack, NJ, 2011.
[7] Chen, B.-Y., Mihai, I., Isometric immersions of contact Riemannian manifolds in real space
forms, Houston J. Math., 31(2005), 743-764
[8] Chen B.-Y., Vrancken, L., CR-submanifolds of
complex hyperbolic spaces satisfying a basic equality, Israel J. Math., 110(1999), 341-358.
[9] Decu, S., Jahanara, B., Petrovic´-Torgašev, M., Verstraelen, L., On the Chen character of
δ(2)-ideal submanifolds, Krag. J. Math., 32(2009), 37-46.
[10] Dillen, F., Petrovic, M., Verstraelen, L., Einstein, conformally flat and semi-symmetric
submanifolds satisfying Chen’s equality, Israel J. Math., 100(1997), 163-169.
[11] Duggal, K. L., Warped product of lightlike manifolds, Nonlinear Analysis, 47(2001), no.5,
3061-3072.
[12] Duggal, K. L., On existence of canonical screens for coisotropic submanifolds, Int. Electron.
J. Geom., 1(2008), no.1, 25-32.
[13] Duggal, K. L., Bejancu, A., Lightlike submanifolds of semi-Riemannian manifolds and
applications, Math. and Its Appl., Kluwer Academic Publisher, Dordrecht, 1996.
[14] Duggal, K. L., Jin, D. H., Totally umbilical lightlike submanifolds, Kodai Math. J.,
26(2003), no.1, 49-68.
[15] Duggal, K. L., On scalar curvature in lightlike geometry, J. of Geo. and Phys., 57(2007),
no.2, 473-481.
[16] Duggal, K. L., Sahin, B., Differential Geometry of Lightlike Submanifolds, Birkhäuser, Basel,
2010.
[17] Fastenakels, J., Ideal tubular hypersurfaces in real space forms, Arch. Math. (Brno),
42(2006), 295-305.
[18] Gülbahar, M., Kılıç, E., Keles¸, S., Chen-like inequalities on lightlike hypersurfaces of a
Lorentzian manifold, J. Inequal. Appl., 2013:266, (2013).
[19] Gülbahar, M., Kılıç, E., Keles¸, S., Some inequalities on screen homothetic lightlike
hypersurfaces of a Lorentzian manifold, Taiwan J. of Math., 17(2013), no.6, 2083-2100.
[20] Hong, S., Matsumoto, K., Tripathi, M. M., Certain basic inequalities for submanifolds of
locally conformal Kaehlerian space forms, SUT J. Math., 4(2005), 75-94.
[21] Jin, D. H., Geometry of coisotropic submanifolds, J. Korea Soc. Math. Educ. Ser. B: Pure
Appl. Math., 8(2001), no.1, 33-46.
[22] Kılıç, E., S¸ ahin, S., Karadag¯ , H. B., Günes¸, R., Coisotropic submanifolds of a
semi-Riemannian manifold, Turk J. Math., 28(2004), 335-352.
[23] Kupeli, D. N., Singular Semi-Riemannian Geometry, Kluwer Academic, 1996.
[24] Mihai, I., Ideal C-totally real submanifolds in Sasakian space forms, Ann. Mat. Pura Appl.,
4(2003), no.182, 345-355.
[25] Mihai, I., Ideal Kaehlerian slant submanifolds in complex space forms, Rocky Mountain J.
Math., 35(2005), no.3, 941-952.
[26] Özgür, C., Arslan, K., On some class of hypersurfaces in En+1 satisfying Chen’s equality, Turk J. Math., 26(2002), 283-293.
[27] Özgür, C., Tripathi, M. M., On submanifolds satisfying Chen’s equality in a real space form,
The Arab. J. for Sci. and Eng., 33(2008), Number 2A, 320-330.
[28] Özgür, C., B.-Y. Chen inequalities for submanifolds of a Riemannian manifold of
quasi-constant curvature, Turk J. Math., 35(2011), no.3, 501-509.
[29] Özgür, C., De, U. C., Chen inequalities for submanifolds of a Riemannian manifold of nearly
quasi-constant curvature, Pub. Math. Debrecen, 82(2013), no. 2, 439-450.
[30] Sahin, B., Screen conformal submersions between lightlike manifolds and semi-Riemannian
manifolds and their harmonicity, Int. J. Geom.Methods Mod. Phys., 4(2007), no.6, 987-1003.
[31] Sasahara, T., CR-submanifolds in a complex hyperbolic space satisfying an equality of Chen,
Tsukuba J. Math., 23(1999), 565-583.
[33] Tripathi, M. M., Certain basic inequalities for submanifolds in (κ, µ) space, Recent advances
in Riemannian and Lorentzian geometries (Baltimore, MD, 2003), Editors K. L. Duggal and R. Sharma,
Amer. Math. Soc., Providence, RI, Contemp. Math., 337(2003), 187-202.
[34] Tripathi, M. M., Kim, J. S., Kim, S. B., A note on Chen’s basic equality for submanifolds in
a Sasakian space form, Int. J. Math. Math. Sci., (2003), no. 11, 711-716.
[35] Vilcu, G. E., B.-Y. Chen inequalities for slant submanifolds in quaternionic space forms,
Turk J. Math. 34(2010), 115-128.
[36] Vilcu, G. E., On Chen invariants and inequalities in quaternionic geometry, J. of Inequal. Appl., 2013:66, (2013).
[37] Zhang, P., Remarks on Chen’s inequalities for submanifolds of a Riemannian manifold of nearly
quasi-constant curvature, Vietnam J. of Math., 43(2015), no.3, 557-569.
[38] Zhang, P., Zhang, L., Song, W., Chen’s inequalities for submanifolds of a Riemannian manifold
of quasi-constant curvature with a semi-symmetric metric connection, Taiwan J. Math., 18(2014), no. 6, 1841-1862.
Ideality of a Coisotropic Lightlike Submanifold
Year 2016,
Volume: 9 Issue: 1, 89 - 99, 30.04.2016
[1] Bejan, C. L., Duggal, K. L., Global lightlike manifolds and harmonicity, Kodai Math. J.,
28(2005), 131-145.
[2] Chen, B.-Y., Some pinching and classification theorems for minimal submanifolds, Arch. Math.
(Brno), 60(1993), 568-578.
[3] Chen, B-Y., Strings of Riemannian invariants, inequalities, ideal immersions and their
applications, in: The Third Pacific Rim Geom. Conf.
Internat Press, Cambridge, MA, (1998), 7-60.
[4] Chen, B.-Y., Riemannian DNA, inequalities and their applications, Tamkang J. of Sci. and Eng.,
3(2000), no.3, 123-130.
[5] Chen, B.-Y., Some new obstructions to minimal and Lagrangian isometric immersions, Japan. J.
Math., 26(2000), 105-127.
[6] Chen, B.-Y., Pseudo-Riemannian geometry, δ-invariants and applications, World Scientific
Publishing, Hackensack, NJ, 2011.
[7] Chen, B.-Y., Mihai, I., Isometric immersions of contact Riemannian manifolds in real space
forms, Houston J. Math., 31(2005), 743-764
[8] Chen B.-Y., Vrancken, L., CR-submanifolds of
complex hyperbolic spaces satisfying a basic equality, Israel J. Math., 110(1999), 341-358.
[9] Decu, S., Jahanara, B., Petrovic´-Torgašev, M., Verstraelen, L., On the Chen character of
δ(2)-ideal submanifolds, Krag. J. Math., 32(2009), 37-46.
[10] Dillen, F., Petrovic, M., Verstraelen, L., Einstein, conformally flat and semi-symmetric
submanifolds satisfying Chen’s equality, Israel J. Math., 100(1997), 163-169.
[11] Duggal, K. L., Warped product of lightlike manifolds, Nonlinear Analysis, 47(2001), no.5,
3061-3072.
[12] Duggal, K. L., On existence of canonical screens for coisotropic submanifolds, Int. Electron.
J. Geom., 1(2008), no.1, 25-32.
[13] Duggal, K. L., Bejancu, A., Lightlike submanifolds of semi-Riemannian manifolds and
applications, Math. and Its Appl., Kluwer Academic Publisher, Dordrecht, 1996.
[14] Duggal, K. L., Jin, D. H., Totally umbilical lightlike submanifolds, Kodai Math. J.,
26(2003), no.1, 49-68.
[15] Duggal, K. L., On scalar curvature in lightlike geometry, J. of Geo. and Phys., 57(2007),
no.2, 473-481.
[16] Duggal, K. L., Sahin, B., Differential Geometry of Lightlike Submanifolds, Birkhäuser, Basel,
2010.
[17] Fastenakels, J., Ideal tubular hypersurfaces in real space forms, Arch. Math. (Brno),
42(2006), 295-305.
[18] Gülbahar, M., Kılıç, E., Keles¸, S., Chen-like inequalities on lightlike hypersurfaces of a
Lorentzian manifold, J. Inequal. Appl., 2013:266, (2013).
[19] Gülbahar, M., Kılıç, E., Keles¸, S., Some inequalities on screen homothetic lightlike
hypersurfaces of a Lorentzian manifold, Taiwan J. of Math., 17(2013), no.6, 2083-2100.
[20] Hong, S., Matsumoto, K., Tripathi, M. M., Certain basic inequalities for submanifolds of
locally conformal Kaehlerian space forms, SUT J. Math., 4(2005), 75-94.
[21] Jin, D. H., Geometry of coisotropic submanifolds, J. Korea Soc. Math. Educ. Ser. B: Pure
Appl. Math., 8(2001), no.1, 33-46.
[22] Kılıç, E., S¸ ahin, S., Karadag¯ , H. B., Günes¸, R., Coisotropic submanifolds of a
semi-Riemannian manifold, Turk J. Math., 28(2004), 335-352.
[23] Kupeli, D. N., Singular Semi-Riemannian Geometry, Kluwer Academic, 1996.
[24] Mihai, I., Ideal C-totally real submanifolds in Sasakian space forms, Ann. Mat. Pura Appl.,
4(2003), no.182, 345-355.
[25] Mihai, I., Ideal Kaehlerian slant submanifolds in complex space forms, Rocky Mountain J.
Math., 35(2005), no.3, 941-952.
[26] Özgür, C., Arslan, K., On some class of hypersurfaces in En+1 satisfying Chen’s equality, Turk J. Math., 26(2002), 283-293.
[27] Özgür, C., Tripathi, M. M., On submanifolds satisfying Chen’s equality in a real space form,
The Arab. J. for Sci. and Eng., 33(2008), Number 2A, 320-330.
[28] Özgür, C., B.-Y. Chen inequalities for submanifolds of a Riemannian manifold of
quasi-constant curvature, Turk J. Math., 35(2011), no.3, 501-509.
[29] Özgür, C., De, U. C., Chen inequalities for submanifolds of a Riemannian manifold of nearly
quasi-constant curvature, Pub. Math. Debrecen, 82(2013), no. 2, 439-450.
[30] Sahin, B., Screen conformal submersions between lightlike manifolds and semi-Riemannian
manifolds and their harmonicity, Int. J. Geom.Methods Mod. Phys., 4(2007), no.6, 987-1003.
[31] Sasahara, T., CR-submanifolds in a complex hyperbolic space satisfying an equality of Chen,
Tsukuba J. Math., 23(1999), 565-583.
[33] Tripathi, M. M., Certain basic inequalities for submanifolds in (κ, µ) space, Recent advances
in Riemannian and Lorentzian geometries (Baltimore, MD, 2003), Editors K. L. Duggal and R. Sharma,
Amer. Math. Soc., Providence, RI, Contemp. Math., 337(2003), 187-202.
[34] Tripathi, M. M., Kim, J. S., Kim, S. B., A note on Chen’s basic equality for submanifolds in
a Sasakian space form, Int. J. Math. Math. Sci., (2003), no. 11, 711-716.
[35] Vilcu, G. E., B.-Y. Chen inequalities for slant submanifolds in quaternionic space forms,
Turk J. Math. 34(2010), 115-128.
[36] Vilcu, G. E., On Chen invariants and inequalities in quaternionic geometry, J. of Inequal. Appl., 2013:66, (2013).
[37] Zhang, P., Remarks on Chen’s inequalities for submanifolds of a Riemannian manifold of nearly
quasi-constant curvature, Vietnam J. of Math., 43(2015), no.3, 557-569.
[38] Zhang, P., Zhang, L., Song, W., Chen’s inequalities for submanifolds of a Riemannian manifold
of quasi-constant curvature with a semi-symmetric metric connection, Taiwan J. Math., 18(2014), no. 6, 1841-1862.
Kılıç, E., & Gülbahar, M. (2016). Ideality of a Coisotropic Lightlike Submanifold. International Electronic Journal of Geometry, 9(1), 89-99. https://doi.org/10.36890/iejg.591898
AMA
Kılıç E, Gülbahar M. Ideality of a Coisotropic Lightlike Submanifold. Int. Electron. J. Geom. April 2016;9(1):89-99. doi:10.36890/iejg.591898
Chicago
Kılıç, Erol, and Mehmet Gülbahar. “Ideality of a Coisotropic Lightlike Submanifold”. International Electronic Journal of Geometry 9, no. 1 (April 2016): 89-99. https://doi.org/10.36890/iejg.591898.
EndNote
Kılıç E, Gülbahar M (April 1, 2016) Ideality of a Coisotropic Lightlike Submanifold. International Electronic Journal of Geometry 9 1 89–99.
IEEE
E. Kılıç and M. Gülbahar, “Ideality of a Coisotropic Lightlike Submanifold”, Int. Electron. J. Geom., vol. 9, no. 1, pp. 89–99, 2016, doi: 10.36890/iejg.591898.
ISNAD
Kılıç, Erol - Gülbahar, Mehmet. “Ideality of a Coisotropic Lightlike Submanifold”. International Electronic Journal of Geometry 9/1 (April 2016), 89-99. https://doi.org/10.36890/iejg.591898.
JAMA
Kılıç E, Gülbahar M. Ideality of a Coisotropic Lightlike Submanifold. Int. Electron. J. Geom. 2016;9:89–99.
MLA
Kılıç, Erol and Mehmet Gülbahar. “Ideality of a Coisotropic Lightlike Submanifold”. International Electronic Journal of Geometry, vol. 9, no. 1, 2016, pp. 89-99, doi:10.36890/iejg.591898.
Vancouver
Kılıç E, Gülbahar M. Ideality of a Coisotropic Lightlike Submanifold. Int. Electron. J. Geom. 2016;9(1):89-9.