Invariant, anti-invariant and slant submanifolds of a metallic manifold

Abstract

Properties of invariant, anti-invariant and slant isometrically immersed submanifolds of metallic Riemannian manifolds are given with a special view towards the induced Σ-structure. Examples of such metallic manifolds are also given.

Submanifolds of almost poly-Norden Riemannian manifolds

“…Hence, we get the following. Inspired from the examples constructed for the golden case [13] and the metallic case [3,10,14], we give the following examples:…”

“…Since the metallic structure on the ambient Riemannian (or semi-Riemannian) manifold provides more general geometric results than the consequences provided by the golden structure on submanifolds, the metallic Riemannian (as well as semi-Riemannian) manifolds have been studied by many authors. Invariant, antiinvariant, semiinvariant, slant, and semislant submanifolds of a metallic Riemannian manifold were studied in [3,10,11]. Some special types of lightlike submanifolds on a metallic semi-Riemannian manifold were introduced in [1,6].…”

On some types of lightlike submanifolds of golden semi-Riemannian manifolds

“…Metallic structure on the ambient Riemannian manifold provides important geometrical results on the submanifolds, since it is an important tool while investigating the geometry of submanifolds. Invariant, anti-invariant, semi-invariant, slant, semi-slant and hemi-slant submanifolds of a Metallic Riemannian manifold are studied in [5,[26][27][28] and the authors obtained important characterizations for submanifolds of Metallic Riemannian manifolds.…”

Totally umbilical proper slant submanifolds of para-Kenmotsu manifold

“…Since then many research articles have been appeared on the existence of different contact and lorentzian manifolds (See. [1,3,7,14,15]).…”

“…[1] Let M be a submanifold of an almost contact metric manifoldM such that ξ ∈ TM. Then, M is slant if and only if there exists a constant λ ∈ [0, 1] such thatP 2 = −λ(I − η ⊗ ξ).…”