Randers Ricci soliton homogeneous nilmanifolds
نویسندگان
چکیده
Let $F$ be a left invariant Randers metric on simply connected nilpotent Lie group $N$, induced by Riemannian ${\hat{\textbf{\textit{a}}}}$ and vector field $X$ which is $I_{\hat{\textbf{\textit{a}}}}(M)$-invariant. If the Ricci flow equation has unique solution then, $(N,F)$ soliton if only semialgebraic soliton.
منابع مشابه
On 5-dimensional 2-step homogeneous randers nilmanifolds of Douglas type
In this paper we first obtain the non-Riemannian Randers metrics of Douglas type on two-step homogeneous nilmanifolds of dimension five. Then we explicitly give the flag curvature formulae and the $S$-curvature formulae for the Randers metrics of Douglas type on these spaces. Moreover, we prove that the only simply connected five-dimensional two-step homogeneous Randers nilmanifolds of D...
متن کاملThe Ricci Flow for Nilmanifolds
We consider the Ricci flow for simply connected nilmanifolds, which translates to a Ricci flow on the space of nilpotent metric Lie algebras. We consider the evolution of the inner product with respect to time and the evolution of structure constants with respect to time, as well as the evolution of these quantities modulo rescaling. We set up systems of O.D.E.’s for some of these flows and des...
متن کاملOn Randers metrics of reversible projective Ricci curvature
projective Ricci curvature. Then we characterize isotropic projective Ricci curvature of Randers metrics. we also show that Randers metrics are PRic-reversible if and only if they are PRic-quadratic../files/site1/files/0Abstract2.pdf
متن کاملA note on Kähler-Ricci soliton
In this note we provide a proof of the following: Any compact KRS with positive bisectional curvature is biholomorphic to the complex projective space. As a corollary, we obtain an alternative proof of the Frankel conjecture by using the Kähler-Ricci flow. The purpose of this note is to give a proof of the following theorem, which does not rely on the previous solutions of Frankel conjecture: T...
متن کاملExpanding Maps on Infra-nilmanifolds of Homogeneous Type
In this paper we investigate expanding maps on infra-nilmanifolds. Such manifolds are obtained as a quotient E\L, where L is a connected and simply connected nilpotent Lie group and E is a torsion-free uniform discrete subgroup of LoC, with C a compact subgroup of Aut(L). We show that if the Lie algebra of L is homogeneous (i.e., graded and generated by elements of degree 1), then the correspon...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematica Scandinavica
سال: 2021
ISSN: ['0025-5521', '1903-1807']
DOI: https://doi.org/10.7146/math.scand.a-122610