Symmetry in Complex Sasakian Manifolds

Year 2020, Volume: 8 Issue: 2, 349 - 354, 27.10.2020

Aysel Vanli , Keziban Avcu

Abstract

In this paper, we give some results on complex Sasakian manifolds. In addition, we introduce a complex $\eta -$Einstein Sasakian manifold. We study on conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor on complex Sasakian manifolds. Moreover, we examine such manifolds under the symmetry conditions with related to special curvature tensors like as conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor. Furthermore, we present some properties of these curvature tensors for a complex Sasakian manifold.

Keywords

complex contact manifolds, complex Sasakian manifolds, symmetry conditions

References

• [1] D: E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, 2nd edn. Birkh¨auser,Boston (2010).
• [2] D. E. Blair and V. M. Molina, Bochner and conformal flatness on normal complex contact metric manifolds, Ann Glob Anal Geom 39, (2011) 249–258 .
• [3] D. E. Blair and A. Turgut Vanli, Corrected energy of distributions for 3-Sasakian and normal complex contact manifolds, Osaka Journal of Mathematics, 43, (2006) 193–200.
• [4] B. J. Foreman, Complex contact manifolds and hyperk¨ahler geometry, Kodai Mathematical Journal, 23, (2000) 12–26.
• [5] S. Ishihara and M. Konishi, Complex almost contact structures in a complex contact manifold, Kodai Mathematical Journal, 5, (1982) 30–37.
• [6] B. Korkmaz, Normality of complex contact manifolds, Rocky Mountain J. Math. 30, (2000) 1343–1380.
• [7] A. Turgut Vanli and D. E. Blair, The boothby-wang fibration of the iwasawa manifold as a critical point of the energy, Monatshefte f¨ur Mathematik, 147, (2006) 75–84.
• [8] A. Turgut Vanli and I. Unal, Ricci semi-symmetric normal complex contact metric manifolds. Italian Journal of Pure and Applied Mathematics,N. 43 (2020) 477–491.
• [9] A. Turgut Vanli and I. Unal, Conformal, concircular, quasi-conformal and conharmonic flatness on normal complex contact metric manifolds, International Journal of Geometric Methods in Modern Physics, 14, (2017) 1750067.
• [10] A. Turgut Vanli and I. Unal, On complex h-Einstein normal complex contact metric manifolds, Communications in Mathematics and Applications, 8, (2017) 301–313.
• [11] A. Turgut Vanli and I. Unal, H-curvature tensors on IK-normal complex contact metric manifolds, International Journal of Geometric Methods in Modern Physics, 15, (2018) 1850205.
• [12] A. Turgut Vanli, I. Unal, and D. Ozdemir, Normal complex contact metric manifolds admitting a semi symmetric metric connection. AppliedMathematics and Nonlinear Sciences, 5,(2020) 49-66.
• [13] A. Turgut Vanli, I. Unal and K. Avcu, On Complex Sasakian manifolds, preprint, Afrika Matematika, doi.org/10.1007/s13370-020-00840-y (2020).