On quasi-Sasakian 3-manifolds admitting η-Ricci solitons
TL;DR: In this paper, it was shown that in a quasi-Sasakian 3-manifold admitting Ricci soliton, the structure function is a constant, which is the same as in the present paper.
Abstract: The object of the present paper is to prove that in a quasi-Sasakian
3-manifold admitting ?-Ricci soliton, the structure function ? is a
constant. As a consequence we obtain several important results.
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TL;DR: In this article, the curvature properties of Ricci solitons on para-Kenmotsu manifolds were studied, and the authors obtained some results of η-Ricci solITons on R(ξ,X).
Abstract: In the present paper, we study curvature properties of η-Ricci solitons on para-Kenmotsu manifolds. We obtain some results of η-Ricci solitons on para-Kenmotsu manifolds satisfying R(ξ,X).C = 0, R(ξ,X).M̃ = 0, R(ξ,X).P = 0, R(ξ,X).C̃ = 0 and R(ξ,X).H = 0, where C, M̃ , P , C̃ and H are a quasi-conformal curvature tensor, a M -projective curvature tensor, a pseudo-projective curvature tensor, and a concircular curvature tensor and conharmonic curvature tensor, respectively.
4 citations
TL;DR: In this article , the existence of ∗ - η -Ricci-Yamabe solitons in a 5-dimensional Sasakian manifold has been proved through a concrete example.
Abstract: In this note, we characterize Sasakian manifolds endowed with ∗ - η -Ricci-Yamabe solitons. Also, the existence of ∗ - η -Ricci-Yamabe solitons in a 5-dimensional Sasakian manifold has been proved through a concrete example.
4 citations
TL;DR: In this paper , the authors studied the properties of invariant submanifolds of hyperbolic Sasakian manifolds and proved that a 3D invariant Submanifold of a 5D hyperskakian manifold is geodesic if and only if it is invariant.
Abstract: We set the goal to study the properties of invariant submanifolds of the
hyperbolic Sasakian manifolds. It is proven that a three-dimensional
submanifold of a hyperbolic Sasakian manifold is totally geodesic if and
only if it is invariant. Also, we discuss the properties of
?-Ricci-Bourguignon solitons on invariant submanifolds of the hyperbolic
Sasakian manifolds. Finally, we construct a non-trivial example of a
three-dimensional invariant submanifold of five-dimensional hyperbolic
Sasakian manifold and validate some of our results.
3 citations
TL;DR: In this paper, the geometrical bearing on Legendrian submanifolds of Sasakian space forms in terms of r-almost Newton-Ricci solitons with the potential function was established.
Abstract: We establish the geometrical bearing on Legendrian submanifolds of Sasakian space forms in terms of r-almost Newton–Ricci solitons (r-anrs) with the potential function $$\psi : M^{n} \rightarrow \mathcal {R}$$
. Also, we discuss the Legendrian immersion of Ricci solitons and obtain conditions for L-minimal and totally geodesic under Newton transformation. Finally, we furnish our paper with the study of 1-anrs on Legendrian submanifolds of Sasakian space form immersed in the locally symmetric Einstein manifolds.
3 citations
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Book•
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
1,822 citations
"On quasi-Sasakian 3-manifolds admit..." refers background in this paper
...Let M be a (2n + 1)-dimensional connected differentiable manifold endowed with an almost contact metric structure (φ, ξ, η, 1), where φ is a tensor field of type (1, 1), ξ is a vector field, η is a 1-form and 1 is the Riemannian metric on M such that ([4], [5]) φ2X = −X + η(X)ξ, (5)...
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Book•
01 Jan 1976
TL;DR: In this paper, the tangent sphere bundle is shown to be a contact manifold, and the contact condition is interpreted in terms of contact condition and k-contact and sasakian structures.
Abstract: Contact manifolds.- Almost contact manifolds.- Geometric interpretation of the contact condition.- K-contact and sasakian structures.- Sasakian space forms.- Non-existence of flat contact metric structures.- The tangent sphere bundle.
1,259 citations
"On quasi-Sasakian 3-manifolds admit..." refers background in this paper
...Let M be a (2n + 1)-dimensional connected differentiable manifold endowed with an almost contact metric structure (φ, ξ, η, 1), where φ is a tensor field of type (1, 1), ξ is a vector field, η is a 1-form and 1 is the Riemannian metric on M such that ([4], [5]) φ2X = −X + η(X)ξ, (5)...
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TL;DR: For supergavrity solutions which are the product of an anti-de Sitter space with an Einstein space X, the relation between the amount of supersymmetry preserved and the geometry of X is studied in this article.
Abstract: For supergavrity solutions which are the product of an anti-de Sitter space with an Einstein space X, we study the relation between the amount of supersymmetry preserved and the geometry of X. Depending on the dimension and the amount of supersymmetry, the following geometries for X are possible, in addition to the maximally supersymmetric spherical geometry: Einstein-Sasaki in dimension 2k+1, 3-Sasaki in dimension 4k+3, 7-dimensional manifolds of weak G_2 holonomy and 6-dimensional nearly Kaehler manifolds. Many new examples of such manifolds are presented which are not homogeneous and have escaped earlier classification efforts. String or M theory in these vacua are conjectured to be dual to superconformal field theories. The brane solutions interpolating between these anti-de Sitter near-horizon geometries and the product of Minkowski space with a cone over X lead to an interpretation of the dual superconformal field theory as the world-volume theory for branes at a conical singularity (cone branes). We propose a description of those field theories whose associated cones are obtained by (hyper-)Kaehler quotients.
398 citations
213 citations
"On quasi-Sasakian 3-manifolds admit..." refers background in this paper
...The notion of quasiSasakian structure was introduced by Blair [6] to unify Sasakian and cosympletic structures....
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