Yapay Zeka Hızlı Bakış & Çıkarımlar
AI InsightWe also obtain somecharacterizations for totally umbilical hypersurfaces and give some examples of invariant and noninvariant hypersurfaces.
📌 3 Maddede Bu Makale
Abstract
Our aim in the present paper is to initiate the study of submanifolds in an almost poly-Norden Riemannianmanifold, which is a new type of manifold first introduced by Şahin [17]. We give fundamental properties of submanifoldsequipped with induced structures provided by almost poly-Norden Riemannian structures and find some conditionsfor such submanifolds to be totally geodesics. We introduce some subclasses of submanifolds in almost poly-NordenRiemannian manifolds such as invariant and antiinvariant submanifolds. We investigate conditions for a hypersurface ofalmost poly-Norden Riemannian manifolds to be invariant and totally geodesic, respectively, by using the components ofthe structure induced by the almost poly-Norden Riemannian structure of the ambient manifold. We also obtain somecharacterizations for totally umbilical hypersurfaces and give some examples of invariant and noninvariant hypersurfaces.