NEW RESULTS ON $(\grave{k},\grave{\mu})$-CONTACT METRIC MANIFOLDS
Abstract
In the present paper we introduce generalized extended $C$-Bochner curvature
tensor on $(\grave{k},\grave{\mu})$-contact metric manifolds. Also, we study
$\grave{\hbar}$-generalized extended $C$-Bochner semisymmetric and $\psi $%
-generalized extended $C$-Bochner semisymmetric non-Sasakian $(\grave{k},%
\grave{\mu})$-contact metric manifolds.
Keywords
Full Text:
PDFReferences
K. Arslan, C. Murathan, C. ¨Ozg¨ur and A. Yıldız: Contact metric R-harmonic manifolds. Balkan J. of Geom. and its Appl. 5 (2000), 1-6.
D. E. Blair: On the geometric meaning of the Bochner Tensor. Geom. Dedicata 4 (1975), 33-38.
D. E. Blair, T. Koufogiorgos and B. J. Papantoniou: Contact metric
manifolds satisfying a nullity condition. Israel Journal of Math. 91 (1995), 189-214.
D. E. Blair: Two remarks on contact metric structures. Tˆohoku Math. J. 29 (1977), 319-324.
S. Bochner: Curvature and Betti numbers. Ann.of Math. (2) 50 (1949), 77-93.
E. Boeckx: A full classification of contact metric (`k, `μ)-spaces. Illinois J. Math. 44 (2000), 212-219.
E. Boeckx, P. Buecken and L. Vanhecke: φ-symmetric contact metric spaces. Glasgow Math. J. 41 (1999), 409-416.
U. C. De, A. A. Shaikh and S. Biswas: On φ-recurrent Sasakian manifolds. Novi Sad J. Math. 33 (2003), 13-48.
H. Endo: On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor. Colloq. Math. Vol. LXII no. 2 (1991), 293-297.
I. Hasegawa and T. Nakane: On Sasakian manifolds with vanishing contact Bochner curvature tensor II. Hokkaido Math. J. 11 (1982), 44-51.
T. Ikawa and M. Kon: Sasakian manifolds with vanishing contact Bochner curvature tensor and constant scalar curvature. Colloq. Math. 37 (1977), 113-122.
O. Kowalski: An explicit classification of 3-dimensional Riemannian spaces satisfying Rcur(X, Y ) · Rcur = 0. Czechoslovak Math. J. 46 (1996), 427-474.
M. Matsumoto and G. Ch¯uman: On the C-Bochner curvature tensor. TRU Math. 5 (1969), 21-30.
B. J. Papantoniou: Contact Riemannian manifolds satifying Rcur(ξ,X) · Rcur = 0 and ξ ∈ (`k, `μ)-nullity distribution. Yokohama Math. J. 40 (1993), 149-161.
T. Takahashi: Sasakian φ-symmetric spaces. Tohoku Math. J. 29 (1977), 91-113.
A. A. Shaikh and K. K. Baishya: On (`k, `μ)-contact metric manifolds. Diff. Geom.- Dynm. System 8 (2006), 253-261.
Z. I. Szabo: Structure theorems on Riemannian manifolds satisfying Rcur(X, Y ) · Rcur = 0, I. Local version, J. Diff. Geo. 17 (1982), 531-582.
S. Tanno: Ricci Curvatures of Contact Riemannian manifolds. Tˆohoku Math. J. 40 (1988), 441-448.
DOI: https://doi.org/10.22190/FUMI240522039Y
Refbacks
- There are currently no refbacks.
ISSN 0352-9665 (Print)