Our aim in the present paper is to initiate the study of submanifolds in an almost poly-Norden Riemannian manifold, which is a new type of manifold first introduced by Şahin . We give fundamental properties of submanifolds equipped with induced structures provided by almost poly-Norden Riemannian structures and find some conditions for such submanifolds to be totally geodesics. We introduce some subclasses of submanifolds in almost poly-Norden Riemannian manifolds such as invariant and antiinvariant submanifolds. We investigate conditions for a hypersurface of almost poly-Norden Riemannian manifolds to be invariant and totally geodesic, respectively, by using the components of the structure induced by the almost poly-Norden Riemannian structure of the ambient manifold. We also obtain some characterizations for totally umbilical hypersurfaces and give some examples of invariant and noninvariant hypersurfaces.
PERKTAŞ, SELCEN YÜKSEL
"Submanifolds of almost poly-Norden Riemannian manifolds,"
Turkish Journal of Mathematics: Vol. 44:
1, Article 3.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss1/3