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Harmonic maps and Riemannian submersions between manifolds endowed with special structures. (English) Zbl 1244.53070

Abramov, Viktor (ed.) et al., Algebra, geometry and mathematical physics. Selected papers based on the presentations at the V Baltic-Nordic workshop on algebra, geometry and mathematical physics, Będlewo, Poland, October 12–16, 2009. Warszawa: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-12-6/pbk). Banach Center Publications 93, 277-288 (2011).
Summary: It is well known that Riemannian submersions are of interest in physics, owing to their applications in Yang-Mills theory, Kaluza-Klein theory, supergravity and superstring theories. In this paper we give a survey of harmonic maps and Riemannian submersions between manifolds equipped with certain geometrical structures such as almost Hermitian structures, contact structures, \(f\)-structures and quaternionic structures. We also present some new results concerning holomorphic maps and semi-Riemannian submersions between manifolds with metric mixed 3-structures.
For the entire collection see [Zbl 1230.53004].

MSC:

53C43 Differential geometric aspects of harmonic maps
53D15 Almost contact and almost symplectic manifolds
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