In this paper, we have studied φ−conformally flat, φ−conharmonicallyflat and φ−projectively flat C−manifolds
Kaynakça
K. Arslan, C. Murathan and C. Ozg¨ur, On φ−Conformally flat contact metric manifolds, Balkan J. Geom. Appl. (BJGA), 5 (2) (2000), 1–7.
K. Arslan, C. Murathan and C. Ozg¨ur, On contact manifolds satisfying certain curvature conditions, Proceedings of the Centennial ”G. Vranceanu” and the Annual Meeting of the Faculty of Mathematics (Bucharest, 2000). An. Univ. Bucure¸sti Mat. Inform., 49 (2) (2000), 17–26.
D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathe- matics, 203. Birkh¨auser Boston, Inc., Boston, MA, 2002.
D. E. Blair., Geometry of manifolds with structural group U (n)xO(s), J. Diff. Geom., 4(1970), 155-167. [5] D. E. Blair., On a generalization of the Hopf fibration, An. St. Univ. ”Al. I. Cuza”Iasi, 17(1971), 171-177. [6] D. E. Blair., G. D. Ludden and K. Yano, Differential geometric structures on principal torodial bundles,Trans. Am. Math. Soc., 181(1973), 175-184.
D. E. Blair, Contact manifolds in Riemannian Geometry, Lecture Notes in Math. Springer– Verlag, Berlin–Heidelberg–New–York, 509 (1976).
J.L. Cabrerizo, L.M. Fernandez, M. Fernandez and G. Zhen, The structure of a class of K–contact manifolds, Acta Math. Hungar, 82 (4) (1999), 331–340.
J.L. Cabrerizo, L.M. Fernandez, M. Fernandez, The curvature tensor fields on f −manifolds with complemented frames, An. ¸st. Univ. ”Al. I. Cuza” Ia¸si Matematica, 36(1990), 151-162. [10] I. Mihai and R. Rosca, On Lorentzian P–Sasakian manifolds, Classical Analysis, World Scientific Publ, Singapore (1992), 155–169.
I. Sato, On a structure similar to almost contact structure, Tensor N.S, 30 (1976), 219–224. [12] I. Sato, On a structure similar to almost contact structure II, Tensor N.S, 31 (1977), 199–205. [13] H. Singh, Q. Khan, On special weakly symmetric Riemannian manifolds, Publ. Math. De- brecen, Hungary 58(2001), 523–536.
C. ¨Ozg¨ur, φ−conformally flat Lorentzian para-Sasakian manifolds, Radovi Mathematicki, 12(2003), 99-106. [15] Y. Ishii, On conharmonic transformations, Tensor N.S, 7 (1957), 73–80.
K. Yano, On a structure defined by a tensor field f of type (1, 1) satisfing f3+ f = 0 Tensor, 14(1963), 99-109. [17] K. Yano and M. Kon, Structures on Manifolds, Series in Pure Math, Vol 3, World Sci, 1984. [18] G. Zhen, On conformal symmetric K–contact manifolds, Chinese Quart. J. of Math, 7 (1992), 5–10.
G. Zhen, J.L. Cabrerizo, L.M. Fernandez and M. Fernandez, On ξ−conformally flat contact metric manifolds, Indian J. Pure Appl. Math, 28 (1997), 725–734.
Aksaray University, Faculty of Art and Sciences, Department of Mathematics, Ak- saray/TURKEY
K. Arslan, C. Murathan and C. Ozg¨ur, On φ−Conformally flat contact metric manifolds, Balkan J. Geom. Appl. (BJGA), 5 (2) (2000), 1–7.
K. Arslan, C. Murathan and C. Ozg¨ur, On contact manifolds satisfying certain curvature conditions, Proceedings of the Centennial ”G. Vranceanu” and the Annual Meeting of the Faculty of Mathematics (Bucharest, 2000). An. Univ. Bucure¸sti Mat. Inform., 49 (2) (2000), 17–26.
D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathe- matics, 203. Birkh¨auser Boston, Inc., Boston, MA, 2002.
D. E. Blair., Geometry of manifolds with structural group U (n)xO(s), J. Diff. Geom., 4(1970), 155-167. [5] D. E. Blair., On a generalization of the Hopf fibration, An. St. Univ. ”Al. I. Cuza”Iasi, 17(1971), 171-177. [6] D. E. Blair., G. D. Ludden and K. Yano, Differential geometric structures on principal torodial bundles,Trans. Am. Math. Soc., 181(1973), 175-184.
D. E. Blair, Contact manifolds in Riemannian Geometry, Lecture Notes in Math. Springer– Verlag, Berlin–Heidelberg–New–York, 509 (1976).
J.L. Cabrerizo, L.M. Fernandez, M. Fernandez and G. Zhen, The structure of a class of K–contact manifolds, Acta Math. Hungar, 82 (4) (1999), 331–340.
J.L. Cabrerizo, L.M. Fernandez, M. Fernandez, The curvature tensor fields on f −manifolds with complemented frames, An. ¸st. Univ. ”Al. I. Cuza” Ia¸si Matematica, 36(1990), 151-162. [10] I. Mihai and R. Rosca, On Lorentzian P–Sasakian manifolds, Classical Analysis, World Scientific Publ, Singapore (1992), 155–169.
I. Sato, On a structure similar to almost contact structure, Tensor N.S, 30 (1976), 219–224. [12] I. Sato, On a structure similar to almost contact structure II, Tensor N.S, 31 (1977), 199–205. [13] H. Singh, Q. Khan, On special weakly symmetric Riemannian manifolds, Publ. Math. De- brecen, Hungary 58(2001), 523–536.
C. ¨Ozg¨ur, φ−conformally flat Lorentzian para-Sasakian manifolds, Radovi Mathematicki, 12(2003), 99-106. [15] Y. Ishii, On conharmonic transformations, Tensor N.S, 7 (1957), 73–80.
K. Yano, On a structure defined by a tensor field f of type (1, 1) satisfing f3+ f = 0 Tensor, 14(1963), 99-109. [17] K. Yano and M. Kon, Structures on Manifolds, Series in Pure Math, Vol 3, World Sci, 1984. [18] G. Zhen, On conformal symmetric K–contact manifolds, Chinese Quart. J. of Math, 7 (1992), 5–10.
G. Zhen, J.L. Cabrerizo, L.M. Fernandez and M. Fernandez, On ξ−conformally flat contact metric manifolds, Indian J. Pure Appl. Math, 28 (1997), 725–734.
Aksaray University, Faculty of Art and Sciences, Department of Mathematics, Ak- saray/TURKEY