On an extended contact Bochner curvature tensor on contact metric manifolds

• Autorzy: Hiroshi Endo
• Języki publikacji: EN

Abstrakty

EN

On Sasakian manifolds, Matsumoto and Chūman [3] defined a contact Bochner curvature tensor (see also Yano [7]) which is invariant under D-homothetic deformations (for D-homothetic deformations, see Tanno [5]). On the other hand, Tricerri and Vanhecke [6] defined a general Bochner curvature tensor with conformal invariance on almost Hermitian manifolds. In this paper we define an extended contact Bochner curvature tensor which is invariant under D-homothetic deformations of contact metric manifolds; we call it the EK-contact Bochner curvature tensor. We show that a contact metric manifold with vanishing EK-contact Bochner curvature tensor is a Sasakian manifold.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1993
• Tom: 65
• Numer: 1
• Strony: 33-41

Daty

wydano

1993

otrzymano

1992-06-24

Twórcy

autor

Hiroshi Endo

• Kohnodai Senior High School, 2-4-1, Kohnodai, Ichikawa-Shi, Chiba-Ken, 272, Japan

Bibliografia

• [1] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer, Berlin 1976.
• [2] D. E. Blair, Critical associated metrics on contact manifolds, J. Austral. Math. Soc. 37 (1984), 82-88.
• [3] M. Matsumoto and G. Chūman, On the C-Bochner tensor, TRU Math. 5 (1969), 21-31.
• [4] Z. Olszak, On contact metric manifolds, Tôhoku Math. J. 31 (1979), 247-253.
• [5] S. Tanno, The topology of contact Riemannian manifolds, Illinois J. Math. 12 (1968), 700-712.
• [6] F. Tricerri and L. Vanhecke, Curvature tensors on almost Hermitian manifolds, Trans. Amer. Math. Soc. 267 (1981), 365-398.
• [7] K. Yano, Anti-invariant submanifolds of a Sasakian manifold with vanishing contact Bochner curvature tensor, J. Differential Geom. 12 (1977), 153-170.
• [8] K. Yano and M. Kon, Structures on Manifolds, World Sci., Singapore 1984.