Hone, Andrew N.W. and Krusch, Steffen (2017) Differential Geometry and Mathematical Physics. In: Analysis and Mathematical Physics. LTCC Advanced Mathematics Series . World Scientific, pp. 140. ISBN 9781786340986. (doi:10.1007/9789402409598) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided) (KAR id:56193)
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Official URL: http://www.worldscientific.com/worldscibooks/10.11... 
Abstract
The chapter will illustrate how concepts in differential geometry arise
naturally in different areas of mathematical physics. We will describe
manifolds, fibre bundles, (co)tangent bundles, metrics and symplectic
structures, and their applications to Lagrangian mechanics, field theory
and Hamiltonian systems, including various examples related to inte
grable systems and topological solitons.
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