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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
Citations
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Geometric inequalities for submanifolds in sasakian space forms
TL;DR: In this article, Carriazo et al. improved Chen's first inequality for special contact slant submanifolds in Sasakian space forms and proved Chen invariants for these intrinsic invariants in terms of the main extrinsic invariant, the squared mean curvature.
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Homogeneous Riemannian structures on some solvable extensions of the Heisenberg group
TL;DR: Two families of four or five-dimensional Riemannian solvable Lie groups, which are extensions of the Heisenberg group, are considered in this article, where all the homogeneous RiemANNian structures on them, and the simply connected groups of isometries corresponding to the associated reductive decompositions, are determined.
An adapted connection on a strict complex contact manifold
TL;DR: In this article, a class of connections on a strict complex almost contact manifold, called adapted connections, is introduced, and adapted connections are used to prove the normality of such a manifold.
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f -BIHARMONIC SUBMANIFOLDS OF GENERALIZED SPACE FORMS
Julien Roth,Abhitosh Upadhyay +1 more
TL;DR: In this paper, the necessary and sufficient condition for f-biharmonicity in generalized complex and Sasakian space forms was studied and some non-existence results were also obtained.
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On a type of contact metric manifolds
Uday Chand De,Pradip Majhi +1 more
TL;DR: In this paper, the authors studied harmonic Weyl conformal curvature tensors, conformally recurrent Ricci tensors and locally o-conformally symmetric contact metric manifolds whose characteristic vector field ξ belonging to the k-nullity distribution.