Warped Product Submanifolds in Locally Golden Riemannian Manifolds with a Slant Factor

Cristina E Hretcanu,Adara M Blaga

doi:10.3390/math9172125

Abstract

In the present paper, we study some properties of warped product pointwise semi-slant and hemi-slant submanifolds in Golden Riemannian manifolds, and we construct examples in Euclidean spaces. Additionally, we study some properties of proper warped product pointwise semi-slant (and, respectively, hemi-slant) submanifolds in a locally Golden Riemannian manifold.

Highlights

Chen studied CR-submanifolds of a Kähler manifold, which are warped products of holomorphic and totally real submanifolds, respectively [1,2,3]. In his new book [4], he presents a multitude of properties for warped product manifolds and submanifolds, such as: warped product of Riemannian and Kähler manifolds, warped product submanifolds of Kähler manifolds, CR-warped products in complex space forms and so on
The authors of the present paper studied some properties of invariant, anti-invariant and slant submanifolds [10], semi-slant submanifolds [11] and, respectively, hemi-slant submanifolds [12] in metallic and Golden Riemannian manifolds and they obtained integrability conditions for the distributions involved in these types of submanifolds
We provide examples of pointwise slant and pointwise bi-slant submanifolds, of warped product semi-slant, hemi-slant and pointwise bi-slant submanifolds in Golden Riemannian manifolds

Summary

Introduction

Chen studied CR-submanifolds of a Kähler manifold, which are warped products of holomorphic and totally real submanifolds, respectively [1,2,3]. The authors of the present paper studied some properties of invariant, anti-invariant and slant submanifolds [10], semi-slant submanifolds [11] and, respectively, hemi-slant submanifolds [12] in metallic and Golden Riemannian manifolds and they obtained integrability conditions for the distributions involved in these types of submanifolds. We study warped product pointwise semi-slant and hemi-slant submanifolds in locally Golden Riemannian manifolds. We provide examples of pointwise slant and pointwise bi-slant submanifolds, of warped product semi-slant, hemi-slant and pointwise bi-slant submanifolds in Golden Riemannian manifolds

Preliminaries

Pointwise Slant Submanifolds in Golden Riemannian Manifolds

Pointwise Bi-Slant Submanifolds in Golden Riemannian Manifolds

Warped Product Pointwise Bi-Slant Submanifolds in Golden Riemannian Manifolds

Warped Product Pointwise Semi-Slant or Hemi-Slant Submanifolds in Golden