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.
Bronze mean, poly-Norden structure, poly-Norden manifold, invariant submanifold, antiinvariant submanifold
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