GJMS operators and Q-curvature for conformal Codazzi structures

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• 作者：Taiji Marugame ^{marugame@ms.u-tokyo.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 53A30 ; secondary ; 53A55
• 刊名：Differential Geometry and its Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：49
• 期：Complete
• 页码：176-196
• 全文大小：440 K

文摘

The conformal Codazzi structure is an intrinsic geometric structure on strictly convex hypersurfaces in a locally flat projective manifold. We construct the GJMS operators and the Q-curvature for conformal Codazzi structures by using the ambient metric. We relate the total Q-curvature to the logarithmic coefficient in the volume expansion of the Blaschke metric, and derive the first and second variation formulas for a deformation of strictly convex domains.