On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor

Hiroshi Endo

Colloquium Mathematicae (1991)

  • Volume: 62, Issue: 2, page 293-297
  • ISSN: 0010-1354

Abstract

top
For Sasakian manifolds, Matsumoto and Chūman [6] defined the contact Bochner curvature tensor (see also Yano [9]). Hasegawa and Nakane [4] and Ikawa and Kon [5] have studied Sasakian manifolds with vanishing contact Bochner curvature tensor. Such manifolds were studied in the theory of submanifolds by Yano ([9] and [10]). In this paper we define an extended contact Bochner curvature tensor in K-contact Riemannian manifolds and call it the E-contact Bochner curvature tensor. Then we show that a K-contact Riemannian manifold with vanishing E-contact Bochner curvature tensor is a Sasakian manifold.

How to cite

top

Endo, Hiroshi. "On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor." Colloquium Mathematicae 62.2 (1991): 293-297. <http://eudml.org/doc/210116>.

@article{Endo1991,
abstract = {For Sasakian manifolds, Matsumoto and Chūman [6] defined the contact Bochner curvature tensor (see also Yano [9]). Hasegawa and Nakane [4] and Ikawa and Kon [5] have studied Sasakian manifolds with vanishing contact Bochner curvature tensor. Such manifolds were studied in the theory of submanifolds by Yano ([9] and [10]). In this paper we define an extended contact Bochner curvature tensor in K-contact Riemannian manifolds and call it the E-contact Bochner curvature tensor. Then we show that a K-contact Riemannian manifold with vanishing E-contact Bochner curvature tensor is a Sasakian manifold.},
author = {Endo, Hiroshi},
journal = {Colloquium Mathematicae},
keywords = {contact Bochner curvature tensor; -contact Riemannian manifolds; Sasakian manifolds},
language = {eng},
number = {2},
pages = {293-297},
title = {On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor},
url = {http://eudml.org/doc/210116},
volume = {62},
year = {1991},
}

TY - JOUR
AU - Endo, Hiroshi
TI - On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor
JO - Colloquium Mathematicae
PY - 1991
VL - 62
IS - 2
SP - 293
EP - 297
AB - For Sasakian manifolds, Matsumoto and Chūman [6] defined the contact Bochner curvature tensor (see also Yano [9]). Hasegawa and Nakane [4] and Ikawa and Kon [5] have studied Sasakian manifolds with vanishing contact Bochner curvature tensor. Such manifolds were studied in the theory of submanifolds by Yano ([9] and [10]). In this paper we define an extended contact Bochner curvature tensor in K-contact Riemannian manifolds and call it the E-contact Bochner curvature tensor. Then we show that a K-contact Riemannian manifold with vanishing E-contact Bochner curvature tensor is a Sasakian manifold.
LA - eng
KW - contact Bochner curvature tensor; -contact Riemannian manifolds; Sasakian manifolds
UR - http://eudml.org/doc/210116
ER -

References

top
  1. [1] D. E. Blair, On the non-existence of flat contact metric structures, Tôhoku Math. J. 28 (1976), 373-379. Zbl0364.53013
  2. [2] D. E. Blair, Two remarks on contact metric structures, ibid. 29 (1977), 319-324. Zbl0376.53021
  3. [3] H. Endo, Invariant submanifolds in a K-contact Riemannian manifold, Tensor (N.S.) 28 (1974), 154-156. 
  4. [4] I. Hasegawa and T. Nakane, On Sasakian manifolds with vanishing contact Bochner curvature tensor II, Hokkaido Math. J. 11 (1982), 44-51. Zbl0485.53041
  5. [5] T. Ikawa and M. Kon, Sasakian manifolds with vanishing contact Bochner curvature tensor and constant scalar curvature, Colloq. Math. 37 (1977), 113-122. Zbl0364.53018
  6. [6] M. Matsumoto and G. Chūman, On the C-Bochner tensor, TRU Math. 5 (1969), 21-30. 
  7. [7] Z. Olszak, On contact metric manifolds, Tôhoku Math. J. 31 (1979), 247-253. 
  8. [8] S. Tanno, The topology of contact Riemannian manifolds, Illinois J. Math. 12 (1968), 700-712. Zbl0165.24703
  9. [9] K. Yano, Anti-invariant submanifolds of a Sasakian manifold with vanishing contact Bochner curvature tensor, J. Differential Geom. 12 (1977), 153-170. Zbl0362.53046
  10. [10] K. Yano, Differential geometry of anti-invariant submanifolds of a Sasakian manifold, Boll. Un. Mat. Ital. 12 (1975), 279-296. Zbl0322.53014
  11. [11] K. Yano and M. Kon, Structures on Manifolds, World Scientific, Singapore 1984. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.