The Decomposition of Global Conformal Invariants : Some Technical

نویسنده

  • Spyros ALEXAKIS
چکیده

This paper forms part of a larger work where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of “global conformal invariants”; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed as a linear combination of a local conformal invariant, a divergence and of the Chern–Gauss–Bonnet integrand.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The decomposition of Global Conformal Invariants: On a conjecture of Deser and Schwimmer

We present a proof of a conjecture of Deser and Schwimmer regarding the algebraic structure of “global conformal invariants”; these are defined to be scalar quantities whose integrals over compact manifolds remain invariant under conformal changes of the underlying metric. We prove that any such invariant can be expressed as a linear combination of a local conformal invariant, a divergence, and...

متن کامل

On the decomposition of Global Conformal Invariants II

This paper is a continuation of [2], where we complete our partial proof of the Deser-Schwimmer conjecture on the structure of “global conformal invariants”. Our theorem deals with such invariants P (g) that locally depend only on the curvature tensor Rijkl (without covariant derivatives). In [2] we developed a powerful tool, the “super divergence formula” which applies to any Riemannian operat...

متن کامل

Conformal mappings preserving the Einstein tensor of Weyl manifolds

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

متن کامل

On the decomposition of Global Conformal Invariants I

This is the first of two papers where we address and partially confirm a conjecture of Deser and Schwimmer, originally postulated in high energy physics, [10]. The objects of study are scalar Riemannian quantities constructed out of the curvature and its covariant derivatives, whose integrals over compact manifolds are invariant under conformal changes of the underlying metric. Our main conclus...

متن کامل

Global Conformal Invariants of Submanifolds

The goal of the present paper is to investigate the algebraic structure of global conformal invariants of submanifolds. These are defined to be conformally invariant integrals of geometric scalars of the tangent and normal bundle. A famous example of a global conformal invariant is the Willmore energy of a surface. In codimension one we classify such invariants, showing that under a structural ...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011