Cotangent Bundles

Jean-Louis Koszul () and Yi Ming Zou
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Jean-Louis Koszul: Université Grenoble Alpes, Institut Fourier
Yi Ming Zou: University of Wisconsin-Milwaukee, Department of Mathematical Sciences

Chapter Chapter 3 in Introduction to Symplectic Geometry, 2019, pp 57-73 from Springer

Abstract: Abstract In this section, we denote by P a manifold, and denote the cotangent bundleCotangent bundle on P by $$T^{*}P$$ . The fiber $$T^{*}_xP$$ of $$T^{*}P$$ at any point $$x\in P$$ is the dual space of the vector space $$T_xP$$ , and the elements in $$T^{*}_xP$$ are the cotangent vectors at the point x. We use $$\pi $$ and $$\pi _{*}$$ to denote the projections of TP and $$T^{*}P$$ on P respectively. We use $$T(T^{*}P)$$ to denote the tangent bundle of the cotangent bundle $$T^{*}P$$ and use $$\pi _0$$ to denote the projection of $$T(T^{*}P)$$ on the base space $$T^{*}P$$ .

Date: 2019
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DOI: 10.1007/978-981-13-3987-5_3

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