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Hessian of the Zeta Function for the Laplacian on Forms

Hessian of the Zeta Function for the Laplacian on Forms Let M be a compact closed n -dimensional manifold. Given a Riemannian metric on M , we consider the zeta functions Z ( s ) for the de Rham Laplacian and the Bochner Laplacian on p -forms. The hessian of Z ( s ) with respect to variations of the metric is given by a pseudodi erential operator T s . When the real part of s is less than n /2−1 we compute the principal symbol of T s . This can be used to determine whether a general critical metric for ( d/ds ) k Z ( s ) has finite index, or whether it is an essential saddle point. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Hessian of the Zeta Function for the Laplacian on Forms

Okikiolu, Kate; Wang, Caitlin
Forum Mathematicum , Volume 17 (1) – Jan 1, 2005
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Publisher
de Gruyter
Copyright
© de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.2005.17.1.105
Publisher site
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Abstract

Let M be a compact closed n -dimensional manifold. Given a Riemannian metric on M , we consider the zeta functions Z ( s ) for the de Rham Laplacian and the Bochner Laplacian on p -forms. The hessian of Z ( s ) with respect to variations of the metric is given by a pseudodi erential operator T s . When the real part of s is less than n /2−1 we compute the principal symbol of T s . This can be used to determine whether a general critical metric for ( d/ds ) k Z ( s ) has finite index, or whether it is an essential saddle point.

Journal

Forum Mathematicum – de Gruyter

Published: Jan 1, 2005

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