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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Journal Article•
TL;DR: In this article, the authors introduce the concept of Golden maps between Riemannian manifolds, and investigate the constancy of these maps by imposing the holomorphic-like map condition.
Abstract: We first introduce Golden maps between Golden Riemannian manifolds,give an example and show that such map is harmonic. Then weinvestigate the constancy of certain maps from Golden Riemannianmanifolds to various manifolds by imposing the holomorphic-like mapcondition. Then we consider the reverse case and show that all suchmaps are constant.
29 citations
Cites background from "Riemannian Geometry of Contact and ..."
...(3) Then (M,φ, ξ, η, g) is called an almost contact metric manifold [3]....
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Dissertation•
01 Jan 2008
TL;DR: A Sasakian manifold S is equipped with a unit-length, Killing vector field which generates a one-dimensional foliation with a transverse Kihler structure as mentioned in this paper.
Abstract: A Sasakian manifold S is equipped with a unit-length, Killing vector field ( which generates a one-dimensional foliation with a transverse Kihler structure. A differential form a on S is called basic with respect to the foliation if it satisfies
28 citations
TL;DR: In this article, a new functional on the space of unit timelike vector fields given by the L 2 norm of the restriction of the covariant derivative of the vector field to its orthogonal complement is defined.
28 citations
Cites background from "Riemannian Geometry of Contact and ..."
...In the Riemannian case it is known (see [3], pg....
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TL;DR: In this paper, the Ricci operator is invariant along the Reeb flow for three-manifolds whose Ricci operators are almost contact invariant, that is, they satisfy £ ξ S = 0.
Abstract: In this paper, we study almost contact three-manifolds M whose Ricci operator is invariant along the Reeb flow, that is, M satisfies £ ξ S = 0 .
28 citations
TL;DR: In this paper, the authors survey what is known about the curvature of exotic spheres and present a survey of the known curvatures of these spheres in terms of their curvatures.
Abstract: Since their discovery by Milnor in 1956, exotic spheres have provided a fascinating object of study for geometers In this article we survey what is known about the curvature of exotic spheres
28 citations