Our aim in this paper is to focus on some applications in differential geometry of the metallic means family (a generalization of the golden mean) and generalized Fibonacci sequences, using a class of polynomial structures defined on Riemannian manifolds. We search for properties of the induced structure on a submanifold by metallic Riemannian structures and we find a necessary and sufficient c...

We show that there exist no proper warped product semi-invariant submanifolds in almost paracontact Riemannian manifolds such that totally geodesic submanifold and totally umbilical submanifold of the warped product are invariant and anti-invariant, respectively. Therefore, we consider warped product semi-invariant submanifolds in the form N N⊥×fNT by reversing two factor manifolds NT and N⊥. W...

In this paper, we would like to study space-like submanifolds in a de Sitter spaces S p (1). We define and discuss three Schrödinger operators LH , LR, LR/H and obtain some spectral characterizations of totally umbilical space-like submanifolds in terms of the first eigenvalue of the Schrödinger operators LH , LR and LR/H respectively.

We give a full classification of Einstein hypersurfaces in irreducible Riemannian symmetric spaces rank greater than 1 (the the rank-one case was previously known). There are two classes such hypersurfaces. The first class consists codimension one solvmanifolds noncompact type constructed via Iwasawa decomposition. second exceptional families low-dimensional $${\overline{M}}=\text {SU}(3)/\text...

For a compact spacelike constant mean curvature surface with nonempty boundary in the threedimensional Lorentz–Minkowski space, we introduce a rotation index of the lines of curvature at the boundary umbilical point, which was developed by Choe [‘Sufficient conditions for constant mean curvature surfaces to be round’, Math. Ann. 323(1) (2002), 143–156]. Using the concept of the rotation index a...

The oriented angles between lightlike vectors cannot be defined properly compared to the timelike in Minkowski spacetime. Therefore, we use pseudo-angles any non-lightlike or develop theory of surfaces having constant angle with a fixed nonlightlike direction. We investigate some geometric properties on these such as being tangent developable. Besides, construct ruled by means null helices. giv...

In this paper, we study locally strongly convex Tchebychev hypersurfaces, namely the {\it centroaffine totally umbilical hypersurfaces}, in $(n+1)$-dimensional affine space $\mathbb{R}^{n+1}$. We first make an ordinary-looking observation that such hypersurfaces are characterized by having a Riemannian structure admitting canonically defined closed conformal vector field. Then, taking advantage...

We consider dimensional reduction of the lightlike holography of the covariant entropy bound from D + 1 dimensional geometry of M × S1 to the D dimensional geometry M . With a warping factor, the local Bekenstein bound in D+ 1 dimensions leads to a more refined form of the bound from the D dimensional view point. With this new local Bekenstein bound, it is quite possible to saturate the lightli...

Massless elementary-particle propagation is represented historically (cosmologically) through 3-scale “towers of quartet rings” within a lattice of magneto-electrodynamically communicating “pre-events”. The lightlike intervals within a ring of 4 pre-events (discrete “closed string”) display transverse GUT-scale and longitudinal “particle scale”. The lightlike (longitudinal) spacing between succ...