Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Positive and negative 3-K-contact structures

Author: Wlodzimierz Jelonek
Journal: Proc. Amer. Math. Soc. 129 (2001), 247-256
MSC (1991): Primary 53C25, 53C15
Published electronically: July 27, 2000
MathSciNet review: 1694866
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The aim of this paper is to give a characterization of 3-K-contact and quasi 3-K-contact manifolds.

References [Enhancements On Off] (What's this?)

  • [B] A. Besse, Einstein Manifolds, Springer-Verlag Berlin, Heidelberg (1987). MR 88f:53087
  • [BGM] C.P. Boyer, K. Galicki, B.M. Mann, The geometry and topology of 3-Sasakian manifolds, J. reine. angew. Math 445 (1994), 183-220. MR 96e:53057
  • [GL] K. Galicki and H.B. Lawson, Quaternionic reduction and Quaternionic Orbifolds, Math. Ann 282 (1988), 1-21. MR 89m:53075
  • [G] A. Gray, Einstein like manifolds which are not Einstein, Geom. Dedicata. 7 (1978), 259-280. MR 80b:53034
  • [I1] S. Ishihara, Quaternion Kählerian manifolds and fibered Riemannian spaces with Sasakian 3-structure, Kodai Math. Sem. Rep. 25 (1973), 321-329. MR 48:2943
  • [I2] S. Ishihara, Quaternion Kählerian manifolds, J. Differential Geom. 9 (1974), 483-500. MR 50:1184
  • [J1] W. Jelonek, Almost Kähler $\mathcal{A}$-structures on twistor bundles, Ann. of Global Analysis and Geometry 17 (1999), 329-339. CMP 99:17
  • [J2] W. Jelonek, Quaternion Kähler geometry and almost Kähler $\mathcal{A}$-manifolds, (to appear in Ann. Polon. Math.).
  • [K] M. Konishi, On manifolds with Sasakian 3 - structures over quaternionic Kähler manifolds, Kodai Math. Sem. Rep. 26 (1975), 194-200. MR 51:13951
  • [Ku] Y-Y. Kuo, On almost contact 3-structures, Tohoku Math. J. 22 (1970), 325-332. MR 43:3956
  • [ON] B. O'Neill, The fundamental equations of a submersion, Mich. Math. J. 13 (1966), 459-469. MR 34:751
  • [S] S. Salamon, Quaternionic Kähler Manifolds, Inv. Math. 67 (1982), 143-171. MR 83k:53054
  • [Sw] A. Swann, Hyperkähler and Quaternionic Kähler geometry, Math. Ann. 289 (1991), 421-450. MR 92c:53030
  • [T] S. Tanno, Remarks on a triple of K-contact structures, Tôhoku Math J. 48 (1996), 519-531. MR 97i:53055

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53C25, 53C15

Retrieve articles in all journals with MSC (1991): 53C25, 53C15

Additional Information

Wlodzimierz Jelonek
Affiliation: Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland

Keywords: 3-K-contact structure, quaternionic-K\"{a}hler manifold, Sasakian structure, $\mathcal{A}$-manifold
Received by editor(s): May 18, 1998
Received by editor(s) in revised form: March 26, 1999
Published electronically: July 27, 2000
Communicated by: Christopher Croke
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society