Titlebook: Holomorphic Curves and Global Questions in Contact Geometry; Casim Abbas,Helmut Hofer Textbook 2019 Springer Nature Switzerland AG 2019 fi

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An Introduction to Contact Geometry,A . on an odd-dimensional manifold . of dimension 2.?+?1 is a one-form . such that the (2.?+?1)-form Ω given by . defines a volume form on .. We observe that any manifold admitting a contact form is necessarily orientable, and that a contact form defines a natural orientation.

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Finite Energy Planes and Periodic Orbits,In this chapter we will prove the main result on finite energy planes due to H. Hofer [.] (see also [.]). Namely, given any manifold . equipped with a contact form ., denote by .?→?. the associated contact structure and by .. the associated Reeb vector field.

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Disk Filling Methods and Applications,Let (., .) be a closed three dimensional contact manifold with overtwisted contact structure .. Then there exists a contractible periodic orbit for the Reeb vector field ...

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