| Full text | |
| Author(s): |
Tojeiro, Ruy
Total Authors: 1
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| Document type: | Journal article |
| Source: | PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY; v. 59, n. 1, p. 247-269, FEB 2016. |
| Web of Science Citations: | 2 |
| Abstract | |
We introduce polar metrics on a product manifold, which have product and warped product metrics as special cases. We prove a de Rham-type theorem characterizing Riemannian manifolds that can be locally or globally decomposed as a product manifold endowed with a polar metric. For such a product manifold, our main result gives a complete description of all its isometric immersions into a space form whose second fundamental forms are adapted to its product structure in the sense that the tangent spaces to each factor are preserved by all shape operators. This is a far-reaching generalization of a basic decomposition theorem for isometric immersions of Riemannian products due to Moore as well as of its extension by Nolker to isometric immersions of warped products. (AU) | |
| FAPESP's process: | 11/21362-2 - Group actions, submanifold theory and global analysis in Riemannian and pseudo-Riemannian geometry |
| Grantee: | Paolo Piccione |
| Support Opportunities: | Research Projects - Thematic Grants |