A note on canonical Ricci forms on $2$-step nilmanifolds
نویسندگان
چکیده
منابع مشابه
A Note on Observability Canonical Forms for Nonlinear Systems
For nonlinear systems affine in the input with state x ∈ R, input u ∈ R and output y ∈ R, it is a well-known fact that, if the function mapping (x, u, . . . , u(n−1)) into (u, . . . , u(n−1), y, . . . , y(n−1)) is an injective immersion, then the system can be locally transformed into an observability normal form with a triangular structure appropriate for a high-gain observer. In this technica...
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 کاملA Canonical Compatible Metric for Geometric Structures on Nilmanifolds
Let (N, γ) be a nilpotent Lie group endowed with an invariant geometric structure (cf. symplectic, complex, hypercomplex or any of their ‘almost’ versions). We define a left invariant Riemannian metric on N compatible with γ to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature. We prove that minimal metrics...
متن کاملOn 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 کاملA Note on Kähler-ricci Flow
Let g(t) with t ∈ [0, T ) be a complete solution to the KaehlerRicci flow: d dt gij̄ = −Rij̄ where T may be ∞. In this article, we show that the curvatures of g(t) is uniformly bounded if the solution g(t) is uniformly equivalet. This result is stronger than the main result in Šešum [6] within the category of Kähler-Ricci flow.
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: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2012-11501-1