On an extended contact Bochner curvature tensor on contact metric manifolds
Colloquium Mathematicae (1993)
- Volume: 65, Issue: 1, page 33-41
- ISSN: 0010-1354
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topEndo, Hiroshi. "On an extended contact Bochner curvature tensor on contact metric manifolds." Colloquium Mathematicae 65.1 (1993): 33-41. <http://eudml.org/doc/210202>.
@article{Endo1993,
abstract = {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.},
author = {Endo, Hiroshi},
journal = {Colloquium Mathematicae},
keywords = {contact Bochner curvature; contact metric manifold; Sasakian manifold},
language = {eng},
number = {1},
pages = {33-41},
title = {On an extended contact Bochner curvature tensor on contact metric manifolds},
url = {http://eudml.org/doc/210202},
volume = {65},
year = {1993},
}
TY - JOUR
AU - Endo, Hiroshi
TI - On an extended contact Bochner curvature tensor on contact metric manifolds
JO - Colloquium Mathematicae
PY - 1993
VL - 65
IS - 1
SP - 33
EP - 41
AB - 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.
LA - eng
KW - contact Bochner curvature; contact metric manifold; Sasakian manifold
UR - http://eudml.org/doc/210202
ER -
References
top- [1] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer, Berlin 1976. Zbl0319.53026
- [2] D. E. Blair, Critical associated metrics on contact manifolds, J. Austral. Math. Soc. 37 (1984), 82-88. Zbl0552.53014
- [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. Zbl0165.24703
- [6] F. Tricerri and L. Vanhecke, Curvature tensors on almost Hermitian manifolds, Trans. Amer. Math. Soc. 267 (1981), 365-398. Zbl0484.53014
- [7] K. Yano, Anti-invariant submanifolds of a Sasakian manifold with vanishing contact Bochner curvature tensor, J. Differential Geom. 12 (1977), 153-170. Zbl0362.53046
- [8] K. Yano and M. Kon, Structures on Manifolds, World Sci., Singapore 1984.
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