Gradient Einstein-Type Structures immersed into a Riemannian Warped Product

E. Batista; L. Adriano; W. Tokura

Gradient Einstein-Type Structures immersed into a Riemannian Warped Product

Differential Geometry 2021-12-30 v3

Authors: E. Batista , L. Adriano , W. Tokura

Abstract

In this paper, we study gradient Einstein-type structure immersed into a Riemannian warped product manifold. We obtain some triviality results for the potential function and smooth map $u$ . We investigate conditions for a gradient Einstein-type structure to be minimal, totally umbilical, or totally geodesic immersed into a warped product $I\times_f M^n$ . Furthermore, we characterize rotational hypersurface into $\mathbb{R}\times_f\mathbb{R}^n$ has a gradient Einstein-type structure.

Keywords

isometric immersions einstein metrics riemannian geometry

Cite

@article{arxiv.2010.02487,
  title  = {Gradient Einstein-Type Structures immersed into a Riemannian Warped Product},
  author = {E. Batista and L. Adriano and W. Tokura},
  journal= {arXiv preprint arXiv:2010.02487},
  year   = {2021}
}

Comments

arXiv admin note: text overlap with arXiv:2010.03995

Related papers

View all related →