Abstract
In this paper, we study some characterizations for any submanifold of a golden Riemannian manifold to be semi-invariant in terms of canonical structures on the submanifold, induced by the golden structure of the ambient manifold. Besides, we determine forms of the distributions involved in the characterizations of a semi-invariant submanifold on both its tangent and normal bundles.
Highlights
The notion of a CR submanifold in Kaehlerian manifolds has been first defined by A
Papaghuic [2] as analogous to that of the CR submanifold, semi-invariant submanifolds in Riemannian manifolds correspond to CR submanifolds in complex manifolds
The main aim of this paper is to investigate some characterizations for any submanifold of a golden Riemannian manifold to be semi-invariant on both its tangent and normal bundles by using canonical structures on the submanifold, induced by the golden structure of the ambient manifold
Summary
The notion of a CR submanifold in Kaehlerian manifolds has been first defined by A. Bejancu [1] as a generalization of both complex and totally real submanifolds Later, this notion has been considered in Riemannian manifolds endowed with almost contact structures. This notion has been considered in Riemannian manifolds endowed with almost contact structures In this sense, the concept of a semi-invariant submanifold in almost contact metric manifolds has been introduced by A. In [20], the notion of a semi-invariant submanifold in golden Riemannian manifolds has been defined by F. The main aim of this paper is to investigate some characterizations for any submanifold of a golden Riemannian manifold to be semi-invariant on both its tangent and normal bundles by using canonical structures on the submanifold, induced by the golden structure of the ambient manifold.
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