# Realizations of some contact metric manifolds as Ricci soliton real hypersurfaces

## TL;DR

This paper demonstrates that certain higher-dimensional contact metric Ricci soliton manifolds with nullity conditions can be realized as homogeneous real hypersurfaces in noncompact real two-plane Grassmannians, confirming their Ricci soliton structure.

## Contribution

It extends the realization of Ricci soliton contact metric manifolds beyond three dimensions as homogeneous hypersurfaces in Grassmannians, using Lie group analysis.

## Key findings

- Higher-dimensional Lie groups are realizable as homogeneous hypersurfaces in Grassmannians.
- All such realizations are Ricci solitons.
- The approach is Lie-theoretic, providing a new perspective on these manifolds.

## Abstract

Ricci soliton contact metric manifolds with certain nullity conditions have recently been studied by Ghosh and Sharma. Whereas the gradient case is well-understood, they provided a list of candidates for the nongradient case.These candidates can be realized as Lie groups, but one only knows the structures of the underlying Lie algebras, which are hard to be analyzed apart from the three-dimensional case. In this paper, we study these Lie groups with dimension greater than three, and prove that the connected, simply-connected, and complete ones can be realized as homogeneous real hypersurfaces in noncompact real two-plane Grassmannians. These realizations enable us to prove, in a Lie-theoretic way, that all of them are actually Ricci soliton.