On an extended contact Bochner curvature tensor on contact metric manifolds

Hiroshi Endo

Colloquium Mathematicae (1993)

  • Volume: 65, Issue: 1, page 33-41
  • ISSN: 0010-1354

Abstract

top
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.

How to cite

top

Endo, 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. [1] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer, Berlin 1976. Zbl0319.53026
  2. [2] D. E. Blair, Critical associated metrics on contact manifolds, J. Austral. Math. Soc. 37 (1984), 82-88. Zbl0552.53014
  3. [3] M. Matsumoto and G. Chūman, On the C-Bochner tensor, TRU Math. 5 (1969), 21-31. 
  4. [4] Z. Olszak, On contact metric manifolds, Tôhoku Math. J. 31 (1979), 247-253. 
  5. [5] S. Tanno, The topology of contact Riemannian manifolds, Illinois J. Math. 12 (1968), 700-712. Zbl0165.24703
  6. [6] F. Tricerri and L. Vanhecke, Curvature tensors on almost Hermitian manifolds, Trans. Amer. Math. Soc. 267 (1981), 365-398. Zbl0484.53014
  7. [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. [8] K. Yano and M. Kon, Structures on Manifolds, World Sci., Singapore 1984. 

NotesEmbed ?

top

You must be logged in to post comments.