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Riemannian Geometry of Contact and Symplectic Manifolds
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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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Book ChapterDOI
A Classification of Ricci Solitons as (k, μ)-Contact Metrics
Amalendu Ghosh,Ramesh Sharma +1 more
TL;DR: In this paper, a non-Sasakian (k, μ)-contact metric g is a Ricci soliton on a (2n + 1)-dimensional smooth manifold M, and (m, g) is locally a three-dimensional Gaussian soliton, or a gradient shrinking rigid Ricci Soliton on the trivial sphere bundle S n (4) × E n+1.
Journal ArticleDOI
Second-Order deformations of associative submanifolds in nearly parallel G2-manifolds
TL;DR: In this paper, it was shown that the infinitesimal deformations of a homogeneous associative submanifold in the 7-sphere given by Lotay, which he called $A_3, are unobstructed to second order.
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Three-dimensional almost Kenmotsu manifolds satisfying certain nullity conditions
TL;DR: In this article, the authors investigate 3-dimensional almost Kenmotsu manifolds satisfying special types of nullity conditions depending on two smooth functions, and obtain examples of quasi-Einstein manifolds.
Journal ArticleDOI
r-Almost Newton–Ricci solitons on Legendrian submanifolds of Sasakian space forms
TL;DR: In this paper, the geometrical bearing on Legendrian submanifolds of Sasakian space forms in terms of r-almost Newton-Ricci solitons with the potential function was established.
Journal ArticleDOI
On Einstein-type contact metric manifolds
TL;DR: In this paper, it was shown that any K-contact manifold admitting an Einstein-type metric is isometric to a unit sphere, and the same conclusion holds for a (k, μ)-contact manifold with zero radial Weyl curvature.