Curvature and torsion of a legendre curve in $(\varepsilon, \delta)$ Trans-Sasakian manifolds
Downloads
DOI:
https://doi.org/10.26637/MJM0601/0018Abstract
In present paper, we obtain curvature and torsion of Legendre curves in 3-dimensional $(\varepsilon, \delta)$ trans-Sasakian manifolds. Also important theorems concerning about biharmonic Legendre curves of $(\varepsilon, \delta)$ trans-Sasakian manifolds have been given.
Keywords:
Legendre curves, Biharmonic mapMathematics Subject Classification:
Mathematics- Pages: 140-144
- Date Published: 01-01-2018
- Vol. 6 No. 01 (2018): Malaya Journal of Matematik (MJM)
A. Bejancu, K. L. Duggal, Real hypersurfaces of indefinite Kahler manifolds, Int. J. Math. Math. Sci., 16(1993), 545-556.
A. A. Balmus, S. Montaldo, C. Onicuic, Biharmonic hypersurfaces in 4-dimensional space forms, Math. Nachr., $283(2010), 1696-1705$.
C. Özgü, M. M. Tripathi, On Legendre curves in $alpha-$ Sasakian manifolds, Bull. Malays. Math. Sci. Soc., 31(2008), 91-96.
D. E. Blair, C. Baikoussis, On Legendre curves in contact 3-manifolds, Geom. Dedicata, 49(1994), 135-142.
D. E. Blair, Riemannian Geometry of Contact and Sympletic Manifolds, Progress in Mathematics 203, Birkhauser Boston, Inc, 2002.
D. Fetcu, C. Onicuic, Explicit formulas for biharmonic submanifolds in non-Euclidean 3-spheres, Abh[. Math. Sem. Univ. Hamburg, 77(2007), 179-190.
D. Fetcu, Biharmonic Legendre curves in Sasakian space form, J. Korean Math. Soc., 45(2008), 393-404.
D. Fetcu, C. Onicuic, Biharmonic hypersurfaces in Sasakian space form, Diff. Geo. Appl., 27(2009), 713722.
D. Fetcu, C. Onicuic, Explicit formulas for biharmonic submanifolds in Sasakian space form, Pacific J. Math., $240(2009), 85-107$
G. Y. Jiang, 2- harmonic maps and their first and second variation formulas, Chinese Ann. Math. Ser. A., 7(1986), $389-402$.
H. G. Nagaraja, G. Somashekara, Special trans-Sasakian manifolds and curvature conditions, Int. J. Pure and Appl. Math., $81(2012), 411-420$.
${ }^{[12]}$ H. G. Nagaraja, R. C. Premalatha, G. Somashekara, On $(varepsilon, delta)$-trans-Sasakian structure, Proceedings of the Estonian Academy of Sciences, 61(2012), 20-28.
I. Inoguchi, Submanifolds with harmonic mean curvature in contact 3-manifolds, Colleq. Math., 100(2004), 163179.
J. Eells, J. H. Sampson, Harmonic mapping of the Riemannian manifold, American J. Math., 86(1964), 109160.
J. Welyczko, On Legendre curves in 3-dimensional normal almost contact metric manifolds, Soochow J. Math., $33(2007), 929-937$.
J. Welyczko, On Legendre curves in 3-dimensional normal almost paracontact metric manifolds, Result. Math., 54(2009), 377-387.
M. M. Tripathi, E. Kılıç, S. Yüksel Perktaş, S. Keleş, Indefinite almost paracontact metric manifods, Int. J. Math. Math. Sci., (2010), Article ID 848195.
R. Kumar, R. Rani, R. K. Nagaich, On sectional curvature of $(varepsilon)$-Sasakian manifolds, Int. J. Math. Math. Sci., (2007), Article ID 93562.
S. Keleş, S. Yüksel Perktaş, E. Kılıç, Biharmonic curves in LP-Sasakian manifolds, Bull. Malays. Math. Sci. Soc., $33(2010), 325-344$.
S. Yüksel Perktaş, E. Kılıç, Biharmonic maps between doubly warped product manifolds, Balkan J. Geom. and Its Appl., 15(2010), 159-170.
S. Yüksel Perktaş, E. Kılıç, S. Keleş, Biharmonic hypersurfaces of Lorentzian para-Sasakian manifolds, $A n$. Stiint. Univ. Al. I. Cuza Iasi., Tomul LVII, f.2 DOI: 10.2478/v10157-011-0034-z, 2011. Hadronic Journal, 32(2009), 231-242.
Hadronic Journal, 32(2009), 231-242.
X. Xufeng, C. Xiaoli, Two theorems on $(varepsilon)$-Sasakian manifolds, Int. J. Math. Math. Sci., 21 (1998), 249-254.
Y. L. Ou, p-Harmonic morphisms, biharmonic morphisms and non-harmonic biharmonic maps, J. Geom. Phys., 56(2006), 358-374.
Y. L. Ou, Biharmonic hypersurfaces in Riemannian manifolds,, Pacific J. Math., 240(2010), 217-232.
Y. L. Ou, Some constructions of biharmonic maps and Chen's conjectures on biharmonic hypersurfaces, $J$. Geom. Phys., 62(2012), 751-762.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2018 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
