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Journal ArticleDOI

Ricci solitons on η-einstein contact manifolds

01 Jan 2018-Filomat (National Library of Serbia)-Vol. 32, Iss: 13, pp 4679-4687
Abstract: The object of the present paper is to study Ricci solitons on η-Einstein contact manifolds. As a consequence of the main result we deduce some important corollaries.
Topics: Einstein (57%)
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Book
01 Jan 1970-

294 citations


References
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Book
08 Jan 2002-
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

1,643 citations


Additional excerpts

  • ...Given the contact metric manifold (M, η, ξ, φ, 1), we have the following identities ([1], [2]): hξ = 0, hφ + φh = 0,...

    [...]

  • ...A (2n + 1)-dimensional manifold M is said to admit an almost contact structure if it admits a tensor field φ of type (1, 1), a vector field ξ and a 1-form η satisfying ([1],[2]) (a) φ2 = −I + η ⊗ ξ, (b) η(ξ) = 1, (c) φξ = 0, (d) η ◦ φ = 0....

    [...]


Book
01 Jan 1976-
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.

1,173 citations


Additional excerpts

  • ...Given the contact metric manifold (M, η, ξ, φ, 1), we have the following identities ([1], [2]): hξ = 0, hφ + φh = 0,...

    [...]

  • ...A (2n + 1)-dimensional manifold M is said to admit an almost contact structure if it admits a tensor field φ of type (1, 1), a vector field ξ and a 1-form η satisfying ([1],[2]) (a) φ2 = −I + η ⊗ ξ, (b) η(ξ) = 1, (c) φξ = 0, (d) η ◦ φ = 0....

    [...]


Book
24 May 2004-
Abstract: The Ricci flow of special geometries Special and limit solutions Short time existence Maximum principles The Ricci flow on surfaces Three-manifolds of positive Ricci curvature Derivative estimates Singularities and the limits of their dilations Type I singularities The Ricci calculus Some results in comparison geometry Bibliography Index.

674 citations


"Ricci solitons on η-einstein contac..." refers background or methods in this paper

  • ...There exist many non-trivial examples of Ricci solitons compact as well as non-compact ([15],[26], [27])....

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  • ...For details we refer to Chow and Knoff [15]....

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Journal ArticleDOI

363 citations


"Ricci solitons on η-einstein contac..." refers background in this paper

  • ...A Riemannian manifold is called locally symmetric [16] if ∇R = 0, where R is the Riemannian curvature tensor of (Mn, 1)....

    [...]


Journal ArticleDOI
Abstract: This paper presents a study of contact metric manifolds for which the characteristic vector field of the contact structure satisfies a nullity type condition, condition (*) below. There are a number of reasons for studying this condition and results concerning it given in the paper: There exist examples in all dimensions; the condition is invariant underD-homothetic deformations; in dimensions>5 the condition determines the curvature completely; and in dimension 3 a complete, classification is given, in particular these include the 3-dimensional unimodular Lie groups with a left invariant metric.

314 citations


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