Journals / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 1997 / Cilt: 46 - Sayı: 1-2
On deformations product
- Journal
- Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
- Pages
- 143–152
- DOI
- —
Abstract
The product of deformations in Riemannian manifolds is defined. The product of infinitesimal isometric deformations (IID) is considered and some results of submanifolds of codimension $geq$ 2 are established. We also study the second fundamental form on the product manifold and prove that the product $M_1 times M_2$ of two hypersurfaces $M_1 subset M_2$ and $M_1 subsetoverline M_1$ , where $overline M_i$ is a Riemannian manifold, i = 1, 2, with a normal IID is a totally geodesic submanifold of $M_1times M_2$ .