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Riemannian Geometry of Contact and Symplectic Manifolds
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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
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Cosymplectic and α-cosymplectic Lie algebras
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Cones of \(G\) manifolds and Killing spinors with skew torsion
Ilka Agricola,Jos Höll +1 more
TL;DR: In this article, the authors studied the cone construction for Riemannian manifolds endowed with an invariant metric connection with skew torsion, a "characteristic connection", and established the explicit correspondence between classes of metric almost contact structures on the cone and almost Hermitian classes on the manifold.
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Magnetic curves on tangent sphere bundles
TL;DR: In this paper, contact magnetic curves on the unit tangent bundle UM of a Riemannian manifold were investigated and the magnetic equations were written in terms of contact normal magnetic curves.
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The $k$-almost Ricci solitons and contact geometry
TL;DR: In this article, the authors studied the k-almost Ricci soliton and k-gradient Ricci s soliton on contact metric manifold and proved that if a compact k-contact metric is a k-approximation to a unit sphere S2n+1, then it is isometric to a sphere S 2 n+1.
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Non-zero contact and Sasakian reduction ✩
TL;DR: In this article, the non-zero case of the contact reduction of Sasakian manifolds was studied and it was shown that Willett's contact reduction is compatible with the Sasakians structure.