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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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28 May 2020
TL;DR: In this article, biharmonic Legendre curves with respect to Schouten-Van Kampen connection have been studied on three-dimensional f-Kenmotsu manifolds.
Abstract: In the present paper, biharmonic Legendre curves with respect to Schouten-Van Kampen connection have been studied on three-dimensional f-Kenmotsu manifolds. Locally $\phi $-symmetric Legendre curves on three-dimensional f-Kenmotsu manifolds with respect to Schouten-Van Kampen Connection have been introduced.Also slant curves have been studied on three-dimensional f-Kenmotsu manifolds with respect to Schouten-Van Kampen connection. Finally, we constract an example of a Legendre curve in a 3-dimensional f-Kenmotsu manifold.
3 citations
TL;DR: The notion of taut contact hyperbola on three-manifolds was introduced in this paper, which is the hyperbolic analogue of the taut circle notion introduced by Geiges and Gonzalo.
Abstract: In this paper, we introduce the notion of taut contact hyperbola on three-manifolds. It is the hyperbolic analogue of the taut contact circle notion introduced by Geiges and Gonzalo (Invent. Math., 121: 147–209, 1995), (J. Differ. Geom., 46: 236–286, 1997). Then, we characterize and study this notion, exhibiting several examples, and emphasizing differences and analogies between taut contact hyperbolas and taut contact circles. Moreover, we show that taut contact hyperbolas are related to some classic notions existing in the literature. In particular, it is related to the notion of conformally Anosov flow, to the critical point condition for the Chern–Hamilton energy functional and to the generalized Finsler structures introduced by R. Bryant. Moreover, taut contact hyperbolas are related to the bi-contact metric structures introduced in D. Perrone (Ann. Global Anal. Geom., 52: 213–235, 2017).
3 citations
TL;DR: In this article, the authors investigate locally φ-conformally symmetric almost Kenmotsu manifolds with their characteristic vector field ξ belonging to some nullity distribution and they give an example of a 5-dimensional almost Ken motsu manifold such that ξ belongs to the (k, μ)′-nullity distribution.
Abstract: The aim of this paper is to investigate locally φ-conformally symmetric almost Kenmotsu manifolds with its characteristic vector field ξ belonging to some nullity distributions. Also, we give an example of a 5-dimensional almost Kenmotsu manifold such that ξ belongs to the (k, μ)′-nullity distribution and h′ 6= 0.
3 citations
TL;DR: In this article, the authors studied a class of almost contact manifolds, namely locally conformal almost manifolds and proved that some of them contain the class of bundle-like metric structures.
Abstract: In this paper, we study a class of almost contact manifolds, namely locally conformal almost manifolds. We investigate subclasses of such manifolds and prove that some of them contain the class of bundle-like metric structures. Under some conditions, we prove that the class of conformal changes of almost cosymplectic structures is a subclass of (almost)-cosymplectic structures. Examples are also obtained.
3 citations
TL;DR: In this article, a generalization of the metric almost contact manifold, called metric f:pk-manifolds, has been proposed, which admits a parallelizable kernel.
Abstract: Abstract We consider a natural generalization of the metric almost contact manifolds that we call metric f:pk-manifolds. They are Riemannian manifolds with a compatible f-structure which admits a parallelizable kernel. With some additional conditions they are called S-manifolds. We give some examples and study some properties of harmonic 1-forms on such manifolds. We also study harmonicity and holomorphicity of vector fields on them.
3 citations
Cites background from "Riemannian Geometry of Contact and ..."
...see [2]) that the normality condition on an almost contact manifold implies the annihilation of certain tensor fields N (2), N (3), N (4)....
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