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Riemannian submersions and related topics. (English) Zbl 1067.53016

River Edge, NJ: World Scientific (ISBN 981-238-896-6/hbk). xiii, 277 p. (2004).
This is a very well written and interesting book on Riemannian submersions and it is the first monograph in the literature about this topic. Here is the abbreviated summary chosen from the preface of the book:
In the first chapter, the basic tools of the theory are given, the main properties of the invariant tensors are stated, together with explicit formulas relating the curvatures of the total space. They also describe some classical examples. The second chapter essentially deals with Riemannian submersions having totally geodesic fibres. Almost Hermitian submersions are investigated in detail in the next chapter. Riemannian submersions between Riemannian manifolds equipped with an almost contact or contact structure are the subject of chapter 4. Chapter 5 concerns with the problem of determining Einstein metrics and Einstein-Weyl structures on manifolds which can be considered as the total space or the base space of a submersion. Using the concept of CR-submanifold of an almost Hermitian in chapter 6 they consider CR-submersions. Chapter 7 deals with semi-Riemannian submersions and the applications of Riemannian submersions in physics are the content of the last chapter.

MSC:

53C20 Global Riemannian geometry, including pinching
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C43 Differential geometric aspects of harmonic maps
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