We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 07 December 2023
In this chapter we introduce foliations and discuss some fundamental examples. We characterise the integrability of subbundles of tangent bundles in terms of both flatness and torsion-freeness of suitable affine connections. In the final section we discuss the simultaneous integrability of complementary distributions making up an almost product structure.
We introduce Bott connections in general, and we apply them to Lagrangian foliations in particular. This leads to a proof of Weinstein’s characterisation of affinely flat manifolds as leaves of Lagrangian foliations. We also prove a Darboux theorem for pairs consisting of a symplectic structure together with a Lagrangian foliation.
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
