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: The higher power derivative terms involved in both Faddeev and Skyrme energy functionals correspond to σ 2 -energy, introduced by Eells and Sampson (1964).
14 citations
TL;DR: In this paper, generalized space forms for contact metric and trans-Sasakian space forms are introduced and studied, and the contact metric case is examined in depth and examples for all possible dimensions.
Abstract: Generalized \({{(\kappa, \mu)}}\)-space forms are introduced and studied. We examine in depth the contact metric case and present examples for all possible dimensions. We also analyse the trans-Sasakian case.
14 citations
TL;DR: A locally symmetric almost Kenmotsu manifold of dimension 2n+1, n ≥ 1, with CR-integrable structure is shown to be locally isometric to either the hyperbolic space of constant sectional curvature −1, or the Riemannian product of an (n + 1)-dimensional manifold of constant (n − 1)-correlations and a flat n-dimensional manifold.
Abstract: In this paper, it is proved that a locally symmetric almost Kenmotsu manifold of dimension 2n+1, n > 1, with CR-integrable structure is locally isometric to either the hyperbolic space of constant sectional curvature −1, or the Riemannian product of an (n + 1)-dimensional manifold of constant sectional curvature −4 and a flat n-dimensional manifold.
14 citations
TL;DR: The notion of biharmonic map between Riemannian manifolds was generalized to maps from RiemANNIAN manifolds into affine manifolds in this article, where Hopf cylinders in 3-dimensional Sasakian space forms which are bi-harmonic with respect to Tanaka-Webster connection were classified.
Abstract: The notion of biharmonic map between Riemannian manifolds is generalized to maps from Riemannian manifolds into affine manifolds. Hopf cylinders in 3-dimensional Sasakian space forms which are biharmonic with respect to Tanaka-Webster connection are classified.
14 citations
Cites methods from "Riemannian Geometry of Contact and ..."
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TL;DR: In this article, the authors considered the Boothby-Wang fibration π : N → N ¯ of a strictly regular Sasakian space form N and found the characterization of biharmonic Hopf cylinders over submanifolds of N ¯.
Abstract: We consider the Boothby–Wang fibration π : N → N ¯ of a strictly regular Sasakian space form N and find the characterization of biharmonic Hopf cylinders over submanifolds of N ¯ . Then, we determine all proper-biharmonic Hopf cylinders over homogeneous real hypersurfaces in complex projective spaces.
14 citations