On the decomposition of global conformal invariants, I
نویسندگان
چکیده
منابع مشابه
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 کاملOn 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 کاملThe Decomposition of Global Conformal Invariants : Some Technical
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 C...
متن کاملThe 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 کاملGlobal 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 ...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2009
ISSN: 0003-486X
DOI: 10.4007/annals.2009.170.1241