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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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Journal ArticleDOI
On Conformally Flat Almost Contact Metric Manifolds
David E. Blair,Handan Yıldırım +1 more
TL;DR: In this paper, a 3D conformally flat almost contact metric manifold with non-constant sectional curvature was constructed and the curvature properties of the manifold were investigated.
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On the Six-dimensional Sphere with a Nearly Kählerian Structure
TL;DR: In this paper, the geometric properties of the six-dimensional sphere with a nearly Kahlerian structure are described, and the authors show that the structure of the sphere can be modeled as a sphere.
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Ricci solitons and gradient ricci solitons on nearly kenmotsu manifolds
Gülhan Ayar,Mustafa Yildirim +1 more
TL;DR: In this article, the Ricci soliton was used to obtain certain conditions about curvature tensors for nearly Kenmotsu manifolds with Ricci-soliton and they obtained certain conditions for curvatures tensors.
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Shape operator of slant submanifolds in sasakian space forms
TL;DR: In this paper, the authors established relations between the sec- tional curvature and the shape operator for a slant submanifold in a Sasakian space form of constant '- sectional curvature with arbi- trary codimension.
Journal ArticleDOI
Ricci almost solitons with associated projective vector field
Ramesh Sharma,Sharief Deshmukh +1 more
TL;DR: In this article , a Ricci almost soliton whose associated vector field is projective is shown to have vanishing Cotton tensor, divergence-free Bach tensor and Ricci tensor as conformal Killing.