Book•
Riemannian Geometry of Contact and Symplectic Manifolds
08 Jan 2002-
TL;DR: 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 Index
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TL;DR: In this article, it was shown that if a complete K-contact manifold M admits a (m, ρ)-quasi-Einstein metric with m ≠ 1, then f is constant and M becomes compact, Einstein and Sasakian.
Abstract: The aim of this note is to prove that if a complete K-contact manifold M of dimension (2n + 1) admits a (m, ρ)-quasi-Einstein metric with m ≠ 1, then we prove that f is constant and M becomes compact, Einstein and Sasakian.
15 citations
TL;DR: In this article, the authors classify certain contact hypersurfaces in the Riemannian symmetric space SU2,m/S(U2Um), m ≥ 3.
Abstract: In this paper, we classify certain contact hypersurfaces in the Riemannian symmetric space SU2,m/S(U2Um), m ≥ 3.
15 citations
TL;DR: In this article, it was shown that if g represents a Ricci soliton whose potential vector field is orthogonal to the Reeb vector field, then M3 is locally isometric to either the hyperbolic space ℍ3(−1) or a non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsusu structure.
Abstract: Abstract Let (M3, g) be an almost Kenmotsu 3-manifold such that the Reeb vector field is an eigenvector field of the Ricci operator. In this paper, we prove that if g represents a Ricci soliton whose potential vector field is orthogonal to the Reeb vector field, then M3 is locally isometric to either the hyperbolic space ℍ3(−1) or a non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsu structure. In particular, when g represents a gradient Ricci soliton whose potential vector field is orthogonal to the Reeb vector field, then M3 is locally isometric to either ℍ3(−1) or ℍ2(−4) × ℝ.
14 citations
Cites background from "Riemannian Geometry of Contact and ..."
...Almost contact metric manifolds can be viewed as an odd-dimensional version of almost Hermitian manifolds (see [2])....
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...Y / (4) for any vector fields X; Y , then M 2nC1 is said to be an almost contact metric manifold and g is said to be a compatible metric with respect to the almost contact structure (see [2])....
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TL;DR: In this article, the relationship between L∞ growth of eigenfunctions and their L 2 concentration as measured by defect measures was studied and it was shown that scarring in the sense of concentration of defect measure on certain submanifolds is incompatible with maximal L ∞ growth.
Abstract: We study the relationship between L∞ growth of eigenfunctions and their L^{2} concentration as measured by defect measures. In particular, we show that scarring in the sense of concentration of defect measure on certain submanifolds is incompatible with maximal L∞ growth. In addition, we show that a defect measure which is too diffuse, such as the Liouville measure, is also incompatible with maximal eigenfunction growth.
14 citations
TL;DR: In this article, the authors define slant submanifolds in neutral almost contact pseudo-metric manifolds, with motivations and examples, and provide some natural examples of the ambient spaces.
Abstract: In this paper we define slant submanifolds in neutral almost contact pseudo-metric manifolds, with motivations and examples. We also provide some natural examples of the ambient spaces.
14 citations