Sasakian metrics as generalized η-Ricci soliton

In this paper, we consider Sasakian metric as a proper η -Ricci almost soliton and prove that it is isometric to a unit sphere S 2 n + 1 , provided the dimension of the manifold is greater than 3. Next, we prove that if a Sasakian manifold admitting a generalized η -Ricci soliton whose potential vec...

Full description

Saved in:
Bibliographic Details
Published in:Periodica mathematica Hungarica 2023-03, Vol.86 (1), p.139-151
Main Author: Ghosh, Amalendu
Format: Article
Language:English
Subjects:
Fields (mathematics)
Mathematics
Mathematics and Statistics
Solitary waves
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we consider Sasakian metric as a proper η -Ricci almost soliton and prove that it is isometric to a unit sphere S 2 n + 1 , provided the dimension of the manifold is greater than 3. Next, we prove that if a Sasakian manifold admitting a generalized η -Ricci soliton whose potential vector field is a contact vector field is η -Einstein and the potential vector field is Killing. Finally, we prove that a complete Sasakian manifold of dimension greater than 3 is isometric to a unit sphere if it admits a non-trivial gradient generalized η -Ricci soliton.
ISSN:0031-5303
1588-2829
DOI:10.1007/s10998-022-00462-w