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Almost contact metric structures on the hypersurface of almost Hermitian manifolds. (English. Russian original) Zbl 1325.53037
J. Math. Sci., New York 207, No. 4, 513-537 (2015); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 127 (2014).
This is a review paper on the theories of almost contact, almost Hermitian and Kenmotsu structures and their use in classical differential geometry. The authors give a very comprehensive account on the historical development of these structures using only Riemannian metrics, although modern applicable studies on these structures have been extended using semi-Riemannian and degenerate metrics for the purpose of their applications. Also, there is a long list of 200 references (which include some minor side references), but, they miss to include the fundamental works of Chen, a 1989 paper of Grey on some global properties of contact structures and S. MacLane [Reports of the Midwest Category Seminar. II. York: Springer-Verlag (1968; Zbl 0165.00201)] on physical applications of contact structures.

MSC:
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C20 Global Riemannian geometry, including pinching
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry
Full Text: DOI
References:
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