Slant and Semi-Slant Submanifolds in Metallic Riemannian Manifolds

Cristina E. Hretcanu,Adara M. Blaga

doi:10.1155/2018/2864263

Abstract

The aim of our paper is to focus on some properties of slant and semi-slant submanifolds of metallic Riemannian manifolds. We give some characterizations for submanifolds to be slant or semi-slant submanifolds in metallic or Golden Riemannian manifolds and we obtain integrability conditions for the distributions involved in the semi-slant submanifolds of Riemannian manifolds endowed with metallic or Golden Riemannian structures. Examples of semi-slant submanifolds of the metallic and Golden Riemannian manifolds are given.

Highlights

In the proposition we find a relation between the slant angles θ of the submanifold M in the metallic Riemannian manifold (M, g, J) and the slant angle θ of the submanifold M in the almost product Riemannian manifold (M, g, F)
For p = q = 1, we obtain the relation between slant angle θ of the immersed submanifold M in a Golden Riemannian manifold (M, g, J) and the slant angle θ of M immersed in the almost product Riemannian manifold (M, g, F)
We obtain that D1 ⊕ D2 is a warped product semi-slant submanifold in the locally Golden Riemannian manifold (R7, ⟨⋅, ⋅⟩, J), with the slant angle arccos((φ +

Summary

Introduction

A.M. Blaga studied the properties of the conjugate connections by a Golden structure and expressed their virtual and structural tensor fields and their behavior on invariant distributions. The properties of the metallic conjugate connections were studied by A.M. Blaga and C.E. Hretcanu in ([23]) where the virtual and structural tensor fields were expressed and their behavior on invariant distributions was analyzed. The purpose of the present paper is to investigate the properties of slant and semi-slant submanifolds in metallic (or Golden) Riemannian manifolds. We have found a relation between the slant angles θ of a submanifold M in a Riemannian manifold (M, g) endowed with a metallic (or Golden) structure J and the slant angle θ of the same submanifold. We have given some examples of semi-slant submanifolds in metallic and Golden Riemannian manifolds

Preliminaries

Submanifolds of Metallic Riemannian Manifolds

Slant Submanifolds in Metallic or Golden Riemannian Manifolds

Semi-Slant Submanifolds in Metallic or Golden Riemannian Manifolds

On the Integrability of the Distributions of Semi-Slant Submanifolds