Geodesic
Sub-Manifolds of a Locally Product Riemannian Manifold
Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 423-435

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In this paper, we have obtained the conditions that a sub-manifold of a locally product Riemannian manifold may also be locally product. Generalizations of the equations of Gauss, Mainardi-Codazzi and Ricci have been obtained for the locally product sub-manifold of the locally product Riemannian manifold. 
Mishra, R. S. Sub-Manifolds of a Locally Product Riemannian Manifold. Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 423-435. doi: 10.4153/CMB-1968-049-1
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     author = {Mishra, R. S.},
     title = {Sub-Manifolds of a {Locally} {Product} {Riemannian} {Manifold}},
     journal = {Canadian mathematical bulletin},
     pages = {423--435},
     year = {1968},
     volume = {11},
     number = {3},
     doi = {10.4153/CMB-1968-049-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-049-1/}
}
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