Riemannian almost product manifolds and submersions. I. II
The first part of the survey contains a presentation of the results concerning the local theory of Riemannian almost product manifolds connected with the group approach to their study [see \textit{A. M. Naveira}, Rend. Mat. Appl., VII. Ser. 3, 577-592 (1983; Zbl 0538.53045)] and the results concerning the global theory of these manifolds based on the Bochner technique. The Introduction and the following Chapters are presented: 2. Classification of the \(GL(n,\mathbb{R})\times GL(m-n,\mathbb{R})\)-structures on an \(m\)-dimensional manifold. 3. \(O(n)\times O(m-n)\)-structures on an \(m\)-dimensional Riemannian manifold and their classification. 4. Weitzenböck formulas for compact Riemannian almost product manifolds. 5. Bochner type theorems in the global geometry of \(O(n)\times O(m-n)\)-structures. The second part contains results of both the local theory of submersions of Riemannian manifolds (except the Riemannian submersions) and the global theory based on the Bochner technique. The Introduction and the following Chapters are presented: 2. Vector-valued forms and special kinds of maps. 3. The second fundamental form of a submersion. 4. Weitzenböck formulas for maps of compact Riemannian manifolds. 5. Bochner type theorems in the global geometry of maps.
scientific article; zbMATH DE number 1506093
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