Research Article
Year 2022,
Volume: 51 Issue: 4, 958 - 969, 01.08.2022
Abstract
References
- [1] F.R. Al-Solamy and S. Uddin, An inequality for warped product submanifolds of a locally product Riemannian manifold, Hacet. J. Math. Stat. 48 (2), 351-358, 2019.
- [2] P. Alegre, B.Y. Chen and M.I. Munteanu, Riemannian submersions, $\delta$ -invariants, and optimal inequality, Ann. Global Anal. Geom. 42 (3), 317-331, 2012.
- [3] C. Atindogbe and K.L. Duggal, Conformal screen on lightlike hypersurfaces, Int. J. Pure Appl. Math. 11, 421442, 2004.
- [4] C.L. Bejan and K.L. Duggal, Global lightlike manifolds and harmonicity, Kodai Math. J. 28, 131-145, 2005.
- [5] B.Y. Chen, A Riemannian invariant for submanifolds in space forms and its applications, World Sci. Publ., River Edge, NJ, 6, 58-81, 1994.
- [6] B.Y. Chen, A series of Kählerian invariants and their applications to Kählerian geometry, Beitr. Algebra Geom. 42, 165-178, 2001.
- [7] B.Y. Chen, Pseudo-Riemannian geometry, $\delta$-invariants and applications, World Scientific 2011.
- [8] S.S. Chern, Minimal submanifolds in a Riemannian manifold, University of Kansas, Department of Mathematics 19, 1968.
- [9] R. Deszcz, M. Gogowska, M. Petrović-Torgašev and L. Verstraelen, On the Roter type of Chen ideal submanifolds, Results Math. 59, 401-413, 2011.
- [10] K.L. Duggal and A. Bejancu, Lightlike submanifolds of semi-Riemannian manifolds and applications, Kluwer Academic Publisher, 1996.
- [11] K.L. Duggal and D.H. Jin, Totally umbilical lightlike submanifolds, Kodai Math. J. 26, 49-68, 2003.
- [12] K.L. Duggal and D.H. Jin, Null curves and hypersurfaces of semi-Riemannian manifolds, World Scientific Publishing, Hackensack, NJ, USA, 2007.
- [13] K.L. Duggal and B. Sahin, Screen Cauchy Riemann lightlike submanifolds, Acta Math. Hungar. 106 (1), 137-165, 2005.
- [14] K.L. Duggal and B. Sahin, Generalized Cauchy Riemann lightlike submanifolds, Acta Math. Hungar. 112 (1-2), 107-130, 2006.
- [15] K.L. Duggal and B. Sahin, Differential geometry of lightlike submanifolds, Birkhäuser Verlag AG. 2010.
- [16] M. Gülbahar, E. Kılıç and S. Keleş, Chen-like inequalities on lightlike hypersurfaces of a Lorentzian manifold, J. Inequal. Appl. 266, 2013.
- [17] D.N. Kupeli, Singular Semi-Riemannian Geometry, Kluwer Academic 1996.
- [18] C. Özgür and C. Murathan, Chen inequalities for submanifolds of a cosymplectic space form with a semi-symmetric metric connection, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 58 (2), 395-408, 2012.
- [19] B. Sahin, Chen’s first inequality for Riemannian maps, Ann. Polon. Math. 117, 249- 258, 2016.
- [20] Z. Şentürk and L. Verstraelen, Chen ideal Kaehler hypersurfaces, Taiwan. J. Math. 12 (7), 1597-1608, 2008.
- [21] V. Slesar, B. Sahin and G.E. Vilcu, Inequalities for the Casorati curvatures of slant submanifolds in quaternionic space forms, J. nequal. Appl. 123, 2014.
- [22] B.D. Suceavă, On strongly minimal Kähler surfaces in ${\mathbf {C}^ 3} $ and the equality ${scal (p)= 4\inf sec (\pi^ r)}$, Results Math. 68 (1-2), 45-69, 2015.
- [23] T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 18, 380-385, 1966.
- [24] F. Tricerri and L. Vanhecke, Curvature tensors on almost Hermitian manifolds, Trans. Am. Math. Soc. 267, 365-398, 1981.
- [25] K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics 3, 1984.
- [26] P. Zhang and L. Zhang, Inequalities for Casorati curvatures of submanifolds in real space forms, Adv. Geom. 16 (3), 329-335, 2016.
Year 2022,
Volume: 51 Issue: 4, 958 - 969, 01.08.2022
Abstract
In this paper, complex lightlike hypersurfaces of an indefinite Kähler manifold are studied. An optimal inequality characterized to strongly minimality for coisotropic lightlike submanifolds is proved. Strongly minimal Monge-type hypersurfaces in $\mathcal{C}_{1}^{4}$ are examined and some examples of these hypersurfaces are given.
References
- [1] F.R. Al-Solamy and S. Uddin, An inequality for warped product submanifolds of a locally product Riemannian manifold, Hacet. J. Math. Stat. 48 (2), 351-358, 2019.
- [2] P. Alegre, B.Y. Chen and M.I. Munteanu, Riemannian submersions, $\delta$ -invariants, and optimal inequality, Ann. Global Anal. Geom. 42 (3), 317-331, 2012.
- [3] C. Atindogbe and K.L. Duggal, Conformal screen on lightlike hypersurfaces, Int. J. Pure Appl. Math. 11, 421442, 2004.
- [4] C.L. Bejan and K.L. Duggal, Global lightlike manifolds and harmonicity, Kodai Math. J. 28, 131-145, 2005.
- [5] B.Y. Chen, A Riemannian invariant for submanifolds in space forms and its applications, World Sci. Publ., River Edge, NJ, 6, 58-81, 1994.
- [6] B.Y. Chen, A series of Kählerian invariants and their applications to Kählerian geometry, Beitr. Algebra Geom. 42, 165-178, 2001.
- [7] B.Y. Chen, Pseudo-Riemannian geometry, $\delta$-invariants and applications, World Scientific 2011.
- [8] S.S. Chern, Minimal submanifolds in a Riemannian manifold, University of Kansas, Department of Mathematics 19, 1968.
- [9] R. Deszcz, M. Gogowska, M. Petrović-Torgašev and L. Verstraelen, On the Roter type of Chen ideal submanifolds, Results Math. 59, 401-413, 2011.
- [10] K.L. Duggal and A. Bejancu, Lightlike submanifolds of semi-Riemannian manifolds and applications, Kluwer Academic Publisher, 1996.
- [11] K.L. Duggal and D.H. Jin, Totally umbilical lightlike submanifolds, Kodai Math. J. 26, 49-68, 2003.
- [12] K.L. Duggal and D.H. Jin, Null curves and hypersurfaces of semi-Riemannian manifolds, World Scientific Publishing, Hackensack, NJ, USA, 2007.
- [13] K.L. Duggal and B. Sahin, Screen Cauchy Riemann lightlike submanifolds, Acta Math. Hungar. 106 (1), 137-165, 2005.
- [14] K.L. Duggal and B. Sahin, Generalized Cauchy Riemann lightlike submanifolds, Acta Math. Hungar. 112 (1-2), 107-130, 2006.
- [15] K.L. Duggal and B. Sahin, Differential geometry of lightlike submanifolds, Birkhäuser Verlag AG. 2010.
- [16] M. Gülbahar, E. Kılıç and S. Keleş, Chen-like inequalities on lightlike hypersurfaces of a Lorentzian manifold, J. Inequal. Appl. 266, 2013.
- [17] D.N. Kupeli, Singular Semi-Riemannian Geometry, Kluwer Academic 1996.
- [18] C. Özgür and C. Murathan, Chen inequalities for submanifolds of a cosymplectic space form with a semi-symmetric metric connection, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 58 (2), 395-408, 2012.
- [19] B. Sahin, Chen’s first inequality for Riemannian maps, Ann. Polon. Math. 117, 249- 258, 2016.
- [20] Z. Şentürk and L. Verstraelen, Chen ideal Kaehler hypersurfaces, Taiwan. J. Math. 12 (7), 1597-1608, 2008.
- [21] V. Slesar, B. Sahin and G.E. Vilcu, Inequalities for the Casorati curvatures of slant submanifolds in quaternionic space forms, J. nequal. Appl. 123, 2014.
- [22] B.D. Suceavă, On strongly minimal Kähler surfaces in ${\mathbf {C}^ 3} $ and the equality ${scal (p)= 4\inf sec (\pi^ r)}$, Results Math. 68 (1-2), 45-69, 2015.
- [23] T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 18, 380-385, 1966.
- [24] F. Tricerri and L. Vanhecke, Curvature tensors on almost Hermitian manifolds, Trans. Am. Math. Soc. 267, 365-398, 1981.
- [25] K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics 3, 1984.
- [26] P. Zhang and L. Zhang, Inequalities for Casorati curvatures of submanifolds in real space forms, Adv. Geom. 16 (3), 329-335, 2016.
There are 26 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | August 1, 2022 |
| Published in Issue | Year 2022 Volume: 51 Issue: 4 |