شماره ركورد كنفرانس :
1151
عنوان مقاله :
Some recent works in higher order geometry
عنوان به زبان ديگر :
Some recent works in higher order geometry
پديدآورندگان :
Suri Ali نويسنده
كليدواژه :
related connections , Banach manifold , Linear connection , Higher order tangent bundle , Connection map , higher order frame bundles , Fr´echet manifold
عنوان كنفرانس :
دومين همايش ملي رياضيات و كاربردهاي آن
چكيده لاتين :
The tangent bundle TkM of order k, of a smooth Banach manifoldM consists of all equivalent
classes of curves that agree up to their accelerations of order k. For a Banach manifold M
and k ∈ N ∪ {0} we prove that TkM admits a vector bundle structure over M if and
only if M is endowed with a linear connection. This bundle structure heavily depends on
the choice of the connection. Then we ask about the extent to which this vector bundle
structure remains isomorphic. To this end we define the notion of the k’th order differential
Tkg : TkM −→ TkN for a given differentiable map g between manifolds M and N. As we
shall see, Tkg becomes a vector bundle morphism if the base manifolds are endowed with
g-related connections. Finally, we construct the principal bundle of linear frames LkM of the vector bundle
TkM over M and we prove that it is the associated bundle to TkM with respect to the
identity representation of GL(Ek).
شماره مدرك كنفرانس :
4475081