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Riemannian Geometry of Contact and Symplectic Manifolds
TLDR
In this article, the authors describe a complex geometry model of Symplectic Manifolds with principal S1-bundles and Tangent Sphere Bundles, as well as a negative Xi-sectional Curvature.Abstract:
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 Indexread more
Citations
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A Generalization of the Boothby-wang Theorem
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A Godbillon-Vey type invariant for a 3-dimensional manifold with a plane field
Vladimir Rovenski,Paweł Walczak +1 more
TL;DR: In this article, a 3-dimensional smooth manifold M equipped with an arbitrary, a priori nonintegrable, distribution (plane field) D and a vector field T transverse to D is considered.
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Strongly stable surfaces in sub-Riemannian 3-space forms
Ana Hurtado,César Rosales +1 more
TL;DR: In this paper, the authors obtained some criteria ensuring strong stability of surfaces in Sasakian 3 -manifolds and obtained new examples of C 1 complete CMC surfaces with empty singular set in the sub-Riemannian 3-space forms by studying those ones containing a vertical line.
Journal ArticleDOI
On Three Dimensional Cosymplectic Manifolds Admitting Almost Ricci Solitons
Uday Chand De,Chiranjib Dey +1 more
TL;DR: In this article, it was shown that in a 3D compact orientable cosymplectic manifold M^3 without boundary, an almost Ricci soliton reduces to Ricci s soliton under certain restriction on the potential function lambda.
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Contact harmonic maps
Sorin Dragomir,Robert Petit +1 more
TL;DR: In this paper, the authors derived the first and second variation formulae for E and study stability of contact harmonic maps, which arise as boundary values of critical points ϕ∈C∞(Ω¯,N) of the functional ∫Ω‖ΠH′ϕ∘ϕ⁎‖2dvol(gB) where Ω⊂Cn+1 is a smoothly bounded strictly pseudoconvex domain endowed with the Bergman metric gB.