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

Abstract

A Cartan space is a pair $(M,K)$, where $M$ is a smooth manifold and $K$

an Hamiltonian on the slit cotangent bundle $T_0^{*}:=TM\ \{(x,0), x\in M\}$ 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 $\mathbb{K} =\{ (x,p)| K(x,p)=1 \}$

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

References

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