A Classification of Ricci Solitons as (k,μ)-Contact Metrics

Authors

Amalendu Ghosh, Chandernagore College
Ramesh Sharma, University of New HavenFollow

Author URLs

Professor Sharma's Faculty Profile

Document Type

Book Chapter

Publication Date

2014

Subject: LCSH

Geometry

Disciplines

Mathematics

Abstract

If a non-Sasakian (k, μ)-contact metric g is a non-trivial Ricci soliton on a (2n + 1)-dimensional smooth manifold M, then (M, g) is locally a three-dimensional Gaussian soliton, or a gradient shrinking rigid Ricci soliton on the trivial sphere bundle S ⁿ(4) × E ⁿ⁺¹, or a non-gradient expanding Ricci soliton with k=0, μ=4. The last case occurs on a Lie group with a left invariant metric, especially for dimension 3, on Sol ³ regarded also as the group E(1, 1) of rigid motions of the Minkowski 2-space.

DOI

10.1007/978-4-431-55215-4_31

Repository Citation

Ghosh, Amalendu and Sharma, Ramesh, "A Classification of Ricci Solitons as (k,μ)-Contact Metrics" (2014). Mathematics Faculty Publications. 8.
https://digitalcommons.newhaven.edu/mathematics-facpubs/8

Publisher Citation

Ghosh, A. Sharma, R. (2014). A Classification of Ricci Solitons as (k, μ)-Contact Metrics. In Real and Complex Submanifolds (pp. 349-358). Springer Japan. DOI: 10.1007/978-4-431-55215-4_31