AN ALMOST $2$-PARACONTACT STRUCTURE ON THE COTANGENT BUNDLE OF A CARTAN SPACE

Authors : M. GİRTU

Pages : 15-22

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Publication Date : 2004-01-01

Article Type : Research Paper

Abstract :A Cartan space is a pair $insert ignore into journalissuearticles values(M,K);$, where $M$ is a smooth manifold and $K$ an Hamiltonian on the slit cotangent bundle $T_0^{*}:=TM\ \{insert ignore into journalissuearticles values(x,0);, x\in M\}$  that is positively homogeneous of degree $1$ in momenta. We show that $K$ induces an almost $2$-paracontact Riemannian structure on $T_0^{*}$ whose restriction to the ¯guratrix bundle $\mathbb{K} =\{ insert ignore into journalissuearticles values(x,p);| Kinsert ignore into journalissuearticles values(x,p);=1 \}$ is an almost paracontact structure. A condition for this almost para- contact structure to be normal is found, and its geometrical meaning is pointed out. Similar results for Finsler spaces can be found in [1] and [3].
Keywords : 2 paracontact structure, Cartan space, Cotangent bundle