Almost-contact structures on hypersurfaces of the tangent bundle of a Riemannian manifold
In the tangent bundle \(T(V_ n)\) of an \(n\)-dimensional Riemannian manifold \(V_ n\), a metric \(G\) is introduced by means of that of \(V_ n\). Let \(M_{2n-1}\) be a hypersurface of \(T(V_ n)\), then there arises a \((\phi,\xi,\eta,g)\)-structure of hyperbolic type. It is a little different in sign of the defining equations from the ordinary almost contact metric structure. This paper mainly treats such hyperbolic \((\phi,\xi,\eta,g)\)-structure on \(M_ 3\subset T(V_ 2)\) and on \(M_ 3\subset T(E_ 2)\) where \(E_ 2\) is a Euclidean space.
almost contact structure of hyperbolic type
scientific article; zbMATH DE number 3915149