Critical point equation on almost f-cosymplectic manifolds

Preface * 1. Symplectic Manifolds * 2. Principal S1-bundles * 3. Contact Manifolds * 4. Associated Metrics * 5. Integral Submanifolds and Contact Transformations * 6. Sasakian and Cosymplectic Manifolds * 7. Curvature of Contact Metric Manifolds * 8. Submanifolds of Kahler and Sasakian Manifolds * 9. Tangent Bundles and Tangent Sphere Bundles * 10. Curvature Functionals and Spaces of Associated Metrics * 11. Negative Xi-sectional Curvature * 12. Complex Contact Manifolds * 13. Additional Topics in Complex Geometry * 14. 3-Sasakian Manifolds * Bibliography * Subject Index * Author Index

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Riemannian Geometry of Contact and Symplectic Manifolds

It is well known that critical points of the total scalar curvature functional ? on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics. When the domain of ? is restricted to the space of constant scalar curvature metrics, there has been a conjecture that a critical point is also Einstein or isometric to a standard sphere. In this paper we prove that n-dimensional critical points have vanishing n− 1 homology under a lower Ricci curvature bound for dimension less than 8.

Critical points of the total scalar curvature functional on the space of metrics of constant scalar curvature

The aim of this article is to study the space of metrics with constant scalar curvature of volume 1 that satisfies the critical point equation for simplicity CPE metrics. It has been conjectured that every CPE metric must be Einstein. Here, we shall focus our attention for 4-dimensional half conformally flat manifolds M4. In fact, we shall show that for a nontrivial must be isometric to a sphere and f is some height function on

Critical point equation on four-dimensional compact manifolds

A note on critical point metrics of the total scalar curvature functional

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Critical point equation on almost f-cosymplectic manifolds

References

Riemannian Geometry of Contact and Symplectic Manifolds

Critical points of the total scalar curvature functional on the space of metrics of constant scalar curvature

Critical point equation on four-dimensional compact manifolds

A note on critical point metrics of the total scalar curvature functional

On almost cosymplectic (κ,μ,ν)-spaces

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