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1
Content available remote Legendre Matrix Method for Legendre Curve in Sasakian 3-Manifold
Aydin Tuba Ağirman, Sezer Mehmet, Kocayiğit Hüseyin
Foundations of Computing and Decision Sciences
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2021
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Vol. 46, No. 3
205--219
EN
In this study, unit-speed the Legendre curves are studied in Sasakian 3-manifold. Firstly, differential equations characterizing the Legendre curves are obtained and the method used for the approximate solution is explained. Then, the approximate solution is found for one of the characterizations of the Legendre curve with the Legendre matrix collocation method. In addition, a sample application is made to make the method more understandable. And finally, with the help of these equations and the approximate solution, the geometric properties of this curve type are examined.
2
Content available remote On totally contact umbilical contact CR-lightlike submanifolds of indefinite Sasakian manifolds
Gogna M., Kumar R., Nagaich R. K.
Demonstratio Mathematica
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2014
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Vol. 47, nr 1
170--178
EN
After brief introduction, we prove that a totally contact umbilical CR-lightlike submanifold is totally contact geodesic. We obtain a necessary and sufficient condition for a CR-lightlike submanifold to be an anti-invariant submanifold. Finally, we characterize a contact CR-lightlike submanifold of indefinite Sasakian manifold to be a contact CR-lightlike product.
3
Content available remote On D-homothetic deformation of trans-Sasakian structure
Shaikh A., Baishya K., Eyasmin S.
Demonstratio Mathematica
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2008
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Vol. 41, nr 1
171-188
EN
The object of the present paper is to study a transformation called D-homothetic deformation of trans-Sasakian structure. Among others it is shown that in a trans-Sasakian manifold, the Ricci operator Q does not commute with the structure tensor phi and the operator Qphi - phiQ is conformal under a D-homothetic deformation. Also the phi-sectional curvature of a trans-Sasakian manifold is conformal under such a deformation. Some non-trivial examples of trans-Sasakian (non-Sasakian) manifolds with global vector fields are obtained.
4
Content available remote CR-submanifolds of a nearly trans-hyperbolic Sasakian manifold
Kumar S., Dube K.
Demonstratio Mathematica
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2008
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Vol. 41, nr 4
921-929
EN
In the present paper we have investigated CR-submanifold of a nearly trans- hyperbolic Sasakian manifold. We have also studied parallel distribution relating to vertical CR-submanifold of a nearly trans- hyperbolic Sasakian manifold.
5
Content available remote Lightlike submanifolds of indefinite quartenion Kaehler manifolds
Sahin B.
Demonstratio Mathematica
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2007
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Vol. 40, nr 3
701-720
EN
We define and study both screen QR-lightlike and screen CR-lightlike submanifolds of an indefinite quaternion Kaehler manifold. We show that screen QR-lightlike submanifolds include quaternion submanifolds and screen CR-lightlike submanifolds include quaternion as well as screen real lightlike submanifolds. We also give some examples of screen QR-lightlike and screen CR-lightlike submanifolds.
6
Content available remote A note on transversal hypersurfaces of Lorentzian almost paracontact manifolds
Prasad R., Rai A., Shukla A., Tripathi M.
Demonstratio Mathematica
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2007
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Vol. 40, nr 4
929-938
EN
Transversal hypersurfaces of Lorentzian almost paracontact manifolds are studied. It is proved that transversal hypersurfaces of Lorentzian almost paracontact manifolds admit an almost product structure and almost product Lorentzian metric structure. We shall also derive a formula which gives the relation between the connection with respect to the Lorentzian metric g and that with respect to induced Lorentzian metric G. Some properties of Lorentzian (f, g, u, v, lambda)-structure, transversal hypersurfaces of Lorentzian cosymplectic manifolds and Lorentzian paracontact Sasakian manifolds are also studied.
7
Content available remote Semi-slant submanifolds of t-manifolds
Khan V., Khan M.
Demonstratio Mathematica
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2006
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Vol. 39, nr 4
907-918
EN
J. L. Cabrerizo et al. [5] studied slant submanifolds of Sasakian and K- contact manifolds. Semi-slant submanifolds were introduced as a generalized version of CR-submanifold. Cabrerizo et al. [4] obtained interesting results for the semi-slant submanifold of Sasakian manifolds. The purpose of the present paper is to study slant and semi-slant submanifolds of a T-manifold.
8
Content available remote On the geometry of hypersurfaces in a quasi-Sasakian manifold
Călin C.
Demonstratio Mathematica
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2003
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Vol. 36, nr 2
451--462
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