Revistes Catalanes amb Accés Obert (RACO)

$G$-structures of second order defined by linear operators satisfying algebraic relations

D. Demetropoulou-Psomopoulou


The present work is based on a type of structures on a differential manifold $V$, called $G$-structures of the second kind, defined by endomorphism $J$ on the second order tangent bundle $T^2(V)$. Our objective is to give conditions for a differential manifold to admit a real almost product and a generalised almost tangent structure of second order. The concepts of the second order frame bundle $H^2(V)$, its structural group $L^2$ and its associated tangent bundle of second order $T^2(V)$ of a differentiable manifold $V$, are used from the point of view that is described in papers \cite{5} and \cite{6}. Also, the almost tangent structure of order two is mentioned and its generalisation, the second order almost transverse structure, is defined.

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