Families of conformally covariant differential operators, Q-curvature and holography

書誌事項

Families of conformally covariant differential operators, Q-curvature and holography

Andreas Juhl

(Progress in mathematics, v. 275)

Birkhäuser, c2009

大学図書館所蔵 件 / 40

この図書・雑誌をさがす

注記

Includes bibliographical reference (p. [469]-484) and index

内容説明・目次

内容説明

A basic problem in geometry is to ?nd canonical metrics on smooth manifolds. Such metrics can be speci?ed, for instance, by curvature conditions or extremality properties, and are expected to contain basic information on the topology of the underlying manifold. Constant curvature metrics on surfaces are such canonical metrics. Their distinguished role is emphasized by classical uniformization theory. Amorerecentcharacterizationofthesemetrics describes them ascriticalpoints of the determinant functional for the Laplacian.The key tool here is Polyakov'sva- ationalformula for the determinant. In higher dimensions, however,it is necessary to further restrict the problem, for instance, to the search for canonical metrics in conformal classes. Here two metrics are considered to belong to the same conf- mal class if they di?er by a nowhere vanishing factor. A typical question in that direction is the Yamabe problem ([165]), which asks for constant scalar curvature metrics in conformal classes. In connection with the problem of understanding the structure of Polyakov type formulas for the determinants of conformally covariant di?erential operators in higher dimensions, Branson ([31]) discovered a remarkable curvature quantity which now is called Branson's Q-curvature. It is one of the main objects in this book.

目次

Spaces, Actions, Representations and Curvature.- Conformally Covariant Powers of the Laplacian, Q-curvature and Scattering Theory.- Paneitz Operator and Paneitz Curvature.- Intertwining Families.- Conformally Covariant Families.

「Nielsen BookData」 より

関連文献: 1件中  1-1を表示

詳細情報

ページトップへ