Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2016, Cilt: 9 Sayı: 1, 89 - 99, 30.04.2016
https://doi.org/10.36890/iejg.591898

Öz

Kaynakça

  • [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.
  • [32] S¸ entürk, Z., Verstraelen, L., Chen ideal Kaehler hypersurfaces. Taiwan J. Math., 12(2008), no.7, 1597-1608.
  • [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

Yıl 2016, Cilt: 9 Sayı: 1, 89 - 99, 30.04.2016
https://doi.org/10.36890/iejg.591898

Öz

The notion of best living way on coisotropic lightlike submanifolds is discussed. Some relations
involving the screen Ricci curvature and the screen scalar curvature are given. Two examples of
coisotropic lightlike submanifolds are mentioned and ideals of leaves of screen distributions in
these examples are investigated by the help of these relations.

Kaynakça

  • [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.
  • [32] S¸ entürk, Z., Verstraelen, L., Chen ideal Kaehler hypersurfaces. Taiwan J. Math., 12(2008), no.7, 1597-1608.
  • [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.
Toplam 38 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Erol Kılıç

Mehmet Gülbahar

Yayımlanma Tarihi 30 Nisan 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 9 Sayı: 1

Kaynak Göster

APA 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. Nisan 2016;9(1):89-99. doi:10.36890/iejg.591898
Chicago Kılıç, Erol, ve Mehmet Gülbahar. “Ideality of a Coisotropic Lightlike Submanifold”. International Electronic Journal of Geometry 9, sy. 1 (Nisan 2016): 89-99. https://doi.org/10.36890/iejg.591898.
EndNote Kılıç E, Gülbahar M (01 Nisan 2016) Ideality of a Coisotropic Lightlike Submanifold. International Electronic Journal of Geometry 9 1 89–99.
IEEE E. Kılıç ve M. Gülbahar, “Ideality of a Coisotropic Lightlike Submanifold”, Int. Electron. J. Geom., c. 9, sy. 1, ss. 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 (Nisan 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 ve Mehmet Gülbahar. “Ideality of a Coisotropic Lightlike Submanifold”. International Electronic Journal of Geometry, c. 9, sy. 1, 2016, ss. 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.