Connected sum construction of constant Q-curvature manifolds in higher dimensions

Yueh Ju Lin

doi:10.1016/j.difgeo.2015.03.001

Connected sum construction of constant Q-curvature manifolds in higher dimensions

Yueh Ju Lin

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

For a compact Riemannian manifold (M, g₂) with constant Q-curvature of dimension n≥6 satisfying nondegeneracy condition, we show that one can construct many examples of constant Q-curvature manifolds by gluing construction. We provide a general procedure of gluing together (M, g₂) with any compact manifold (N, g₁) satisfying a geometric assumption. In particular, we can prove that there exists a metric with constant Q-curvature on the connected sum N#M.

Original language	English (US)
Pages (from-to)	290-320
Number of pages	31
Journal	Differential Geometry and its Application
Volume	40
DOIs	https://doi.org/10.1016/j.difgeo.2015.03.001
State	Published - Jun 1 2015

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology
Computational Theory and Mathematics

Keywords

Conformal geometry
Connected sum
Paneitz operator
Q-curvature

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10.1016/j.difgeo.2015.03.001

Cite this

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abstract = "For a compact Riemannian manifold (M, g2) with constant Q-curvature of dimension n≥6 satisfying nondegeneracy condition, we show that one can construct many examples of constant Q-curvature manifolds by gluing construction. We provide a general procedure of gluing together (M, g2) with any compact manifold (N, g1) satisfying a geometric assumption. In particular, we can prove that there exists a metric with constant Q-curvature on the connected sum N#M.",

keywords = "Conformal geometry, Connected sum, Paneitz operator, Q-curvature",

author = "Lin, {Yueh Ju}",

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doi = "10.1016/j.difgeo.2015.03.001",

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PY - 2015/6/1

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N2 - For a compact Riemannian manifold (M, g2) with constant Q-curvature of dimension n≥6 satisfying nondegeneracy condition, we show that one can construct many examples of constant Q-curvature manifolds by gluing construction. We provide a general procedure of gluing together (M, g2) with any compact manifold (N, g1) satisfying a geometric assumption. In particular, we can prove that there exists a metric with constant Q-curvature on the connected sum N#M.

AB - For a compact Riemannian manifold (M, g2) with constant Q-curvature of dimension n≥6 satisfying nondegeneracy condition, we show that one can construct many examples of constant Q-curvature manifolds by gluing construction. We provide a general procedure of gluing together (M, g2) with any compact manifold (N, g1) satisfying a geometric assumption. In particular, we can prove that there exists a metric with constant Q-curvature on the connected sum N#M.

KW - Conformal geometry

KW - Connected sum

KW - Paneitz operator

KW - Q-curvature

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M3 - Article

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SN - 0926-2245

VL - 40

SP - 290

EP - 320

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

ER -

Connected sum construction of constant Q-curvature manifolds in higher dimensions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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