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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
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The classification of complete stable area-stationary surfaces in the Heisenberg group H1☆
TL;DR: In this paper, it was shown that any C 2 complete, orientable, connected, stable area-stationary surface in the sub-Riemannian Heisenberg group H 1 is either a Euclidean plane or congruent to the hyperbolic paraboloid t = x y.
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Ricci solitons in contact metric manifolds
TL;DR: In this paper, the Ricci solitons with pointwise collinear with the structure vector field were studied in the context of contact metric manifolds and/or $(k,\mu)$-manifolds.
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Certain Contact Metrics as Ricci Almost Solitons
TL;DR: In this paper, it was shown that if a compact K-contact metric is a gradient Ricci almost soliton, then it is isometric to a unit sphere S 2n+1.
Journal ArticleDOI
Slant curves in contact pseudo-hermitian 3-manifolds
Jong Taek Cho,Ji-Eun Lee +1 more
TL;DR: By using the pseudo-Hermitian connection (or Tanaka-Webster connection) b, this article constructed the parametric equations of Legendre pseudo-hermitian circles (whose b-geodesic curvatureb is constant and b r-Geodesic torsionb is zero) in S 3.
Journal ArticleDOI
Sasakian metric as a Ricci soliton and related results
Amalendu Ghosh,Ramesh Sharma +1 more
TL;DR: In this paper, it was shown that the Sasakian metric on the Heisenberg group H 2 n + 1 is a non-trivial Ricci soliton of such type, and that if an η -Einstein contact metric manifold has a vector field V leaving the structure tensor and the scalar curvature invariant, then either V is an infinitesimal automorphism, or M is D -homothetically fixed K -contact.