Turkish Journal of Mathematics
Abstract
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 [17]. 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.
DOI
10.3906/mat-1901-58
Keywords
Bronze mean, poly-Norden structure, poly-Norden manifold, invariant submanifold, antiinvariant submanifold
First Page
31
Last Page
49
Recommended Citation
PERKTAŞ, S. Y (2020). Submanifolds of almost poly-Norden Riemannian manifolds. Turkish Journal of Mathematics 44 (1): 31-49. https://doi.org/10.3906/mat-1901-58
