ON ALMOST r-PARACONTACT RIEMANNIAN MANIFOLD WITH A CERTAIN CONNECTION

Ahmad, Mobin; Haseeb, Abdul; Jun, Jae-Bok; Rahman, Shamsur

doi:10.4134/ckms.2010.25.2.235

Cited by 2 publications

(1 citation statement)

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“…Acet et al [15] studied canonical paracontact connection on a para-Sasakian manifold. Ahmad et al [16] defined a quarter symmetric semi-metric connection in an almost r-paracontact Riemannian manifold and considered invariant, non-invariant, and antiinvariant hypersurfaces of an almost r-paracontact Riemannian manifold with that connection. Nakova and Zamkovoy [17] considered almost paracontact pseudo-Riemannian manifolds with indefinite metric g, which is it compatible with almost paracontact structure and it satisfies the condition.…”

Section: Introductionmentioning

confidence: 99%

Euler-Lagrange Equations With 3-Dimensional Real Number Space on an Almost Paracontact Manifold

2016

Jour. Pure Appl. Math. Adv. Appl.

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We consider Euler-Lagrange equations on almost paracontact manifolds. It is well known that the geometry of almost contact manifolds is a natural extension in the odd dimensional case of almost Hermitian geometry. A Hermitian manifold is a complex manifold with a Hermitian metric on its holomorphic tangent space. Also, the contact geometry as symplectic geometry has large and comprehensive applications in physics, geometrical optics, classical mechanics, thermodynamics, geometric quantization, and applied mathematics. On the other hand, one way of solving problems in classical and analytical mechanics is through use of the Euler-Lagrange equations. The purpose of the present paper is to solve the problems of classical mechanics with 3-dimensional real number space on an almost paracontact manifold by using Euler-Lagrange equations.

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Section: Introductionmentioning

confidence: 99%