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On conharmonic curvature tensor in -contact and Sasakian manifolds.
Mohit Kumar Dwivedi,Jeong-Sik Kim +1 more
- Vol. 34, Iss: 1, pp 171-180
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TLDR
In this paper, it was proved that a compact φ-conharmonically flat K-contact manifold with regular contact vector field is a principal S1-bundle over an almost Kaehler space of constant holomorphic sectional curvature.Abstract:
Some necessary and/or sufficient condition(s) for K-contact and/or Sasakian manifolds to be quasi conharmonically flat, ξ-conharmonically flat and φ-conharmonically flat are obtained. In last, it is proved that a compact φ-conharmonically flat K-contact manifold with regular contact vector field is a principal S1-bundle over an almost Kaehler space of constant holomorphic sectional curvature ( 3− 2 2n−1 ) . 2010 Mathematics Subject Classification: 53C25, 53D10, 53D15read more
Citations
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On t -curvature tensor in k-contact and sasakian manifolds
Mukut Mani Tripathi,Punam Gupta +1 more
TL;DR: In this paper, the necessary and sufficient condition for the K-contact manifold to be ''-T-∞at under some algebraic con- dition was given, and it was proved that a compact ''T -∞-at Kcontact manifold with regular contact vector fleld, under an algebraic condition, is a principal S 1 -bundle over an almost Kaehler space of constant holomorphic sectional curvature.
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Some classes of Kenmotsu manifolds with respect to semi-symmetric metric connection
TL;DR: In this article, the authors studied conharmonic curvature tensor tensor in Kenmotsu manifolds with respect to semi-symmetric metric connection and also characterized conharmonically flat, conharmony semisymmetric and ϕ-conharmony flat manifolds.
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On $(N(k),\xi)$-semi-Riemannian manifolds: Semisymmetries
Mukut Mani Tripathi,Punam Gupta +1 more
TL;DR: In this article, it was shown that a semi-Riemannian manifold is always a semisymmetric manifold, which is defined by a tensor tensor of type 1,3.
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-Homothetic Deformation of -Contact Manifolds
H. G. Nagaraja,C. R. Premalatha +1 more
TL;DR: In this paper, it was shown that a -homothetically deformed contact manifold is a generalized Sasakian space form if and only if it is conharmonically flat.
References
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Book
Riemannian Geometry of Contact and Symplectic Manifolds
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.
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The Structure of a Class of K-contact Manifolds
TL;DR: In this article, it was shown that a compact φ-conformally flat K-contact manifold with regular contact vector field is a principal S1-bundle over an almost Kaehler space of constant holomorphic sectional curvature.