*-Weyl Curvature Tensor within the Framework of Sasakian and $(\kappa,\mu)$-Contact Manifolds

Authors

  • Venkatesha Venkatesha Department Mathematics, Kuvempu University,Shankaraghatta - 577 451, Shimoga, Karnataka, INDIA. https://orcid.org/0000-0002-2799-2535
  • H. Aruna Kumara Dept. of Mathematics, Kuvempu University, Shankaraghatta-577 451, Shivamogga, Karnataka

DOI:

https://doi.org/10.5556/j.tkjm.52.2021.3440

Keywords:

Sasakian manifolds, $(\kappa,\mu)$-contact manifolds, $*$-Ricci tensor, $*$-Weyl curvature tensor

Abstract

The object of the present paper is to study $*$-Weyl curvature tensor within the framework of Sasakian and $(\kappa,\mu)$-contact manifolds.

Author Biography

Venkatesha Venkatesha, Department Mathematics, Kuvempu University,Shankaraghatta - 577 451, Shimoga, Karnataka, INDIA.

Assistant Professor,

Department Mathematics,
Kuvempu University,
Shankaraghatta - 577 451,
Shimoga, Karnataka, INDIA.

References

D. E. Blair, Riemannian geometry of contact and symplectic manifolds. Birkhauser, Boston, 2010.

D. E. Blair, T. Koufogiorgos, B.J. Papantoniou, Contact metric manifolds satisfying a nullity condition. Isr. J. Math. 91 (1995), 189-214.

D. E. Blair and T. Koufogiorgos, When is the tangent sphere bundle conformally flat. J. Geom. 49 (1994), 55-66.

E. Boeckx, A full classification of contact metric (κ,μ)-spaces. Ill. J. Math. 44(2000), 212-219.

C. P. Boyer and K. Galicki, Sasakian Geometry. Oxford University Press, Oxford (2008).

M. C. Chaki and M. Tarafdar, On a type of Sasakian manifold. Soochow J. Math. 16(1) (1990), 23-28.

S. S. Chern, On the curvature and characteristic classes of a Riemannian manifold. Abh. Math. Semin. Univ. Hambg. 20 (1956), 117–126.

A. Ghosh, Conformally recurrent (κ,μ)-contact manifolds. Note Mat. 28(2)(2008), 207-212.

A. Ghosh, T. Koufogiorgos and R. Sharma, Conformally flat contact metric manifolds. J. Geom.70 (2001), 66-76,

A. Ghosh, D. S. Patra, ∗-Ricci Soliton within the framework of Sasakian and (κ,μ)-contact manifold. Int. J. Geom. Methods Mod. Phys. 15(7) (2018), 1850120

T. Hamada, Real hypersurfaces of complex space forms in terms of Ricci ∗-tensor. Tokyo J. Math. 25 (2002), 473-483.

A. K. Huchchappa, D.M. Naik and V. Venkatesha, Certain results on contact metric generalized (κ, μ)-space forms, Commun. Korean Math. Soc. 34 (4) (2019), 1315-1328.

T. A. Ivey and P. J. Ryan, The ∗-Ricci tensor for hypersurfaces in CPn and CHn. Tokyo J. Math. 34 (2011), 445-471.

G. Kaimakamis and K. Panagiotidou, On a new type of tensor on real hypersurfaces in non-flat complex space forms. Symmetry 2019, 11(4), 559; https://doi.org/10.3390/sym11040559.

T. Miyazawa and S. Yamaguchi, Some theorems on K-contact metric manifolds and Sasakian manifolds. TRU Math. 2 (1966), 46-52.

M. Okumura, Some remarks on spaces with certain contact structures. Tohoku Math. J. 14 (1962), 135-145.

S. Tachibana, On almost-analytic vectors in almost Kahlerian manifolds. Tohoku Math. J. 11 (1959), 247-265.

S. Tanno, The topology of contact Riemannian manifolds. Illinois J. Math. 12 (1968), 700- 717.

S. Tanno, Locally symmetric K-contact Riemannian manifolds. Proc. Japan Acad. 43 (1967), 581-583.

H. Weyl, Reine Infinitesimalgeometrie. Math. Z. 2(3-4) (1918), 384-411.

H. Weyl, Zur Infinitesimalgeometrie, Einordnung der projektiven und der konformen Auffassung. Gottingen Nachrichten. (1921), 99–112.

Downloads

Published

2021-08-01

How to Cite

Venkatesha, V., & Kumara, H. A. (2021). *-Weyl Curvature Tensor within the Framework of Sasakian and $(\kappa,\mu)$-Contact Manifolds. Tamkang Journal of Mathematics, 52(3), 383-395. https://doi.org/10.5556/j.tkjm.52.2021.3440

Issue

Section

Papers