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Realizations of some contact metric manifolds as Ricci soliton real hypersurfaces,
The 11th OCAMI-RIRCM Joint Differential Geometry Workshop on Submanifolds and Lie Theory
(大阪市立大学),
2016/03/20-23.
Abstract
Ricci soliton contact metric manifolds with some 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 non-gradient case.
These candidates can be realized as Lie groups,
but one only knows the bracket relations of the Lie algebras, which are hard
to be understood apart from the three-dimensional case.
In this talk,
we will study these spaces with higher-dimensions,
and prove that the simply-connected
ones can be realized as homogeneous real hypersurfaces in noncompact two-plane Grassmannians.
These realizations enable us to prove, in a Lie-theoretic way, that all of them are actually Ricci solitons.
This talk is based on a joint work with
Jong Taek Cho, Takahiro Hashinaga, Akira Kubo, and Yuichiro Taketomi.
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