Dynamical (In)Stability of Ricci-flat ALE metrics along the Ricci flow

نویسندگان

چکیده

We study the stability and instability of ALE Ricci-flat metrics around which a Łojasiewicz inequality is satisfied for variation Perelman’s $$\lambda $$ functional adapted to situation denoted _{{\text {ALE}}}$$ . This was introduced by authors in recent work it has been proven that satisfies good enough at least neighborhoods integrable dimension larger than or equal 5.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Numerical Ricci - flat metrics on K 3

We develop numerical algorithms for solving the Einstein equation on Calabi-Yau manifolds at arbitrary values of their complex structure and Kähler parameters. We show that Kähler geometry can be exploited for significant gains in computational efficiency. As a proof of principle, we apply our methods to a one-parameter family of K3 surfaces constructed as blow-ups of the T /Z2 orbifold with ma...

متن کامل

Dynamic Instability of Cp under Ricci Flow

The intent of this short note is to provide an independent proof of the unpublished discovery of Klaus Kröncke [Kro13] that complex projective space with its canonical Fubini–Study metric is dynamically unstable under Ricci flow in all complex dimensions N ≥ 2. The unstable perturbation is not Kähler. This provides a counterexample to a well known conjecture widely attributed to Hamilton. Moreo...

متن کامل

ADIABATIC LIMITS OF RICCI - FLAT KÄHLER METRICS 3 from

We study adiabatic limits of Ricci-flat Kähler metrics on a Calabi-Yau manifold which is the total space of a holomorphic fibration when the volume of the fibers goes to zero. By establishing some new a priori estimates for the relevant complex Monge-Ampère equation, we show that the Ricci-flat metrics collapse (away from the singular fibers) to a metric on the base of the fibration. This metri...

متن کامل

Ricci-flat supertwistor spaces

We show that supertwistor spaces constructed as a Kähler quotient of a hyperkähler cone (HKC) with equal numbers of bosonic and fermionic coordinates are Ricci-flat, and hence, Calabi-Yau. We study deformations of the supertwistor space induced from deformations of the HKC. We also discuss general infinitesimal deformations that preserve Ricci-flatness.

متن کامل

On Ricci flat supermanifolds

We study the Ricci flatness condition on generic supermanifolds. It has been found recently that when the fermionic complex dimension of the supermanifold is one the vanishing of the super-Ricci curvature implies the bosonic submanifold has vanishing scalar curvature. We prove that this phenomena is only restricted to fermionic complex dimension one. Further we conjecture that for complex fermi...

متن کامل

ذخیره 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: Calculus of Variations and Partial Differential Equations

سال: 2023

ISSN: ['0944-2669', '1432-0835']

DOI: https://doi.org/10.1007/s00526-022-02403-4