منابع مشابه
Tangent and Cotangent Bundles
of subsets of TM: Note that i) 8 (p;Xp) 2 TM , as p 2M ) there exists (U ; ) 2 S such that p 2 U ; i.e. (p;Xp) 2 TU , and we have TU = 1 (R) 2 : ii) If we de ne F : TpM ! R by F (Xp) = (Xp(x); Xp(x); :::::; Xp(x)) where x; x; ::::; x are local coordinates on (U ; ), then clearly F is an isomorphism, so (p; Xp) = ( (p); F ( Xp)); and 1 = ( 1 ; F 1 ): Now take 1 (U); 1 (V ) 2 and suppos...
متن کاملTangent and Cotangent Bundles
i) 8 (p;Xp) 2 TM , as p 2M ) there exists (U ; ) 2 S such that p 2 U ; i.e. (p;Xp) 2 TU , and we have TU = 1 (R) 2 . ii) If we de ne F : TpM ! R by F (Xp) = (Xp(x); Xp(x); :::::; Xp(x)) where x; x; ::::; x are local coordinates on (U ; ), then clearly F is an isomorphism, so (p; Xp) = ( (p); F ( Xp)); and 1 = ( 1 ; F 1 ). Now take 1 (U); 1 (V ) 2 and suppose (p; Xp) 2 1 (U)\ 1 (V ...
متن کاملMoving Frames for Cotangent Bundles
This paper has a very modest scope: we present our “operational system” for Hamiltonian mechanics on cotangent bundles M = T Q, based on moving frames. In a related work [10], we will present some concrete examples to convey the algorithmical nature of this formalism. A powerful tool in riemannian geometry is the “method of moving frames”, introduced by Élie Cartan. Actually, moving frames appe...
متن کاملOn the Floer homology of cotangent bundles
This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle T M of a compact orientable manifold M . The first result is a new L estimate for the solutions of the Floer equation, which allows to deal with a larger and more natural class of Hamiltonians. The second and main result is a new construction of the isomorphism between the Fl...
متن کاملAutomorphisms of cotangent bundles of Lie groups
Let G be a Lie group, G its Lie algebra, T G its cotangent bundle and D := tG the Lie algebra of T G. We investigate the group of automorphisms of D. More precisely, we fully characterize the space of all derivations of D. As a byproduct, we also characterize some spaces of operators on G amongst which the space J of bi-invariant tensors on G and prove that if G has a bi-invariant Riemannian or...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2009
ISSN: 0026-2285
DOI: 10.1307/mmj/1260475697