Mathematical Sciences: Geometric Approach to Weinstein Conjecture

Project: Research project

Project Details

Description

The principal investigator will study the existence of compact leaves in contact foliations of compact contact manifolds. The existence of these foliations was conjectured by Weinstein. Several special cases have been solved by this investigator and by other mathematicians. Lickorish surgical techniques will be used to investigate the three-dimensional version of the problem. Okumura's theory will be applied to the problem in the case of hypersurfaces with contact types in Kaehler manifolds. Diffeomorphism groups will also be studied. 'Manifolds' are generalized surfaces. These may be filled with collections of lower dimensional 'leaves.' Such collections of leaves are called 'foliations.' The principal investigator will study leaves which do not wrap on continuously but actually close up. These are called in the literature, 'compact leaves.' Such are particularly important in applications to other sciences in that they represent, in a general sense, behavior which repeats indefinitely.

StatusFinished
Effective start/end date7/1/906/30/93

Funding

  • National Science Foundation: $47,650.00

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