A useful orthonormal basis on bi-slant submanifolds of almost Hermitian manifolds

Article Sidebar

PDF
Published: Jun 30, 2016
DOI: https://doi.org/10.5556/j.tkjm.47.2016.1748
Keywords:
Almost Hermitian manifold Slant submanifold Complex space form.

Main Article Content

Mehmet Gulbahar
Erol Kilic
Sadik Keles

Abstract

In this paper, we study bi-slant submanifolds of an almost Hermitian manifold for different cases. We introduce a new orthonormal basis on bi-slant submanifold, semi-slant submanifold and hemi-slant submanifold of an almost Hermitian manifold to compute Chen's main inequalities. We investigate these inequalities for semi-slant submanifolds, hemi-slant submanifolds and slant submanifolds of a generalized complex space form. We obtain some characterizations on such submanifolds of a complex space form.

Article Details

How to Cite
Gulbahar, M., Kilic, E., & Keles, S. (2016). A useful orthonormal basis on bi-slant submanifolds of almost Hermitian manifolds. Tamkang Journal of Mathematics, 47(2), 143–161. https://doi.org/10.5556/j.tkjm.47.2016.1748
Issue
Vol. 47 No. 2 (2016)
Section
Papers
Author Biographies

Mehmet Gulbahar

Siirt University, Science & Arts Faculty, Department ofMathematics, Siirt, Turkey.

Erol Kilic

InönüUniversity, Science & Arts Faculty, Department ofMathematics,Malatya, Turkey.

Sadik Keles

InönüUniversity, Science & Arts Faculty, Department ofMathematics,Malatya, Turkey.

References

J. L. Cabrerizo, A. Carriazo, L. M. Fernandez and M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasg. Math. J., 42(2000), 125--138.

E. Calabi, Isometric embeddings of complex manifolds, Ann. of Math., 58(1953), 1--23.

E. Calabi, Metric Riemann surfaces, Ann. of Math. Studies, 30(1953), 77--85.

A. Carriazo, New developments in slant submanifolds theory, Applicable Mathematics in the Golden Age (Edited by J.C. Misra), Narosa Publishing House (2002), 339--356.

A. Carriazo, Bi-slant immersions, Proceedings ICRAMS (2000), 88--97.

B.-Y. Chen, K. Ogiue, On totally real submanifolds, Trans. Amer. Math. Soc., 193 (1974),257--266.

B.-Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit Leuven, 1990.

B.-Y. Chen, A Riemannian invariant for submanifolds in space forms and its applications. Geometry and Topology of Submanifolds, VI (Leuven, 1993/Brussels, 1993) (NJ: World Scientific Publishing, River Edge) (1994), pp. 58--81 no. 6, 568--578.

A. Gray, Nearly Kahler manifolds}, J. Differ. Geo. 4(1970), 283--309.

H. H. Hacisalihoglu, Lineer Cebir, Hacisalihoglu Yayinlari, Matematik-Geometri Dizisi, 9. Baski, 2010.

S. Hong, M. M. Tripathi, On Ricci curvature of submanifolds, Int. J. Pure and Appl. Sci. 2(2005), 227--246.

J-S. Kim, Y-M. Y-M. Song, M. M. Tripathi, B.-Y. Chen inequalities for submanifolds in generalized complex space forms, Bull. Korean Math. Soc., 40(2003), 411--423.

K. Matsumoto, I. Mihai, A. Oiaga, Ricci curvature of submanifolds in complex space forms, Rev. Roumanie Math. Pures Appl. 46(2001), 775--782.

A. Mihai, B.Y. Chen inequalities for slant submanifolds in generalized complex space forms, Radovi Matemativcki, 12(2004), 215--231.

P. K. Pandey, R. S. Gupta, A. Sharfuddin, B. Y. Chen's inequalities for bi-slant submanifolds in Kenmotsu space forms, Demonstrario Mathematica 18 (2010),

--898.

S. S. Shukla, P. K. Rao, B.Y. Chen inequalities for bi-slant submanifolds in generalized complex space forms, The J. of Nonlinear Sci. and Appl. 3(2010),

--293.

F. Tricerri, L. Vanhecke, Curvature tensors on almost Hermitian manifolds,Trans. Am. Math. Soc., 267(1981), 365--398.

L. Vanhecke, Almost Hermitian manifolds with J-invariant Riemann curvature tensor, Rend. Sem. Mat. Univers. Politec. Torino 34(1975/76), 487--498.

K. Yano, M. Kon, Structures on manifolds, Series in Pure Mathematics, Volume 3, 1984.