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Almost paracontact and parahodge structures on manifolds

Published online by Cambridge University Press:  22 January 2016

Soji Kaneyuki  and
Floyd L. Williams
Soji Kaneyuki
Affiliation:
Sophia University, Tokyo, Kioicho, Chiyoda-ku, Tokyo 102, Japan and University of Massachusetts/Amherst
Floyd L. Williams
Affiliation:
University of Massachusetts/Amherst, Ma. 01003, U.S.A.
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In this paper we study the paracomplex analogues of almost contact structures, and we introduce and study the notion of parahodge structures on manifolds. In particular, we construct new examples of paracomplex manifolds and we find all simply connected parahermitian symmetric coset spaces, which are the adjoint orbits of noncompact simple Lie groups, with parahodge structures induced by the Killing forms. This is done by (i) observing that a version of the results of A. Morimoto [4] on almost contact structures can be formulated and proved for almost paracontact structures, and by (ii) the methods of geometric quantization [3] applied to parahermitian symmetric triples [1] in conjunction with results of [7]. Two of the main results are Theorem 2.5 (which ties together the above structures) and Corollary 3.9.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 99 , September 1985 , pp. 173 - 187
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

References

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