Title

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

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

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