Almost hyper-Hermitian structures in bundle spaces over manifolds with almost contact 3 -structure

Francisco Martín Cabrera

Czechoslovak Mathematical Journal (1998)

  • Volume: 48, Issue: 3, page 545-563
  • ISSN: 0011-4642

Abstract

top
We consider almost hyper-Hermitian structures on principal fibre bundles with one-dimensional fiber over manifolds with almost contact 3-structure and study relations between the respective structures on the total space and the base. This construction suggests the definition of a new class of almost contact 3-structure, which we called trans-Sasakian, closely connected with locally conformal quaternionic Kähler manifolds. Finally we give a family of examples of hypercomplex manifolds which are not quaternionic Kähler.

How to cite

top

Cabrera, Francisco Martín. "Almost hyper-Hermitian structures in bundle spaces over manifolds with almost contact $3$-structure." Czechoslovak Mathematical Journal 48.3 (1998): 545-563. <http://eudml.org/doc/30436>.

@article{Cabrera1998,
abstract = {We consider almost hyper-Hermitian structures on principal fibre bundles with one-dimensional fiber over manifolds with almost contact 3-structure and study relations between the respective structures on the total space and the base. This construction suggests the definition of a new class of almost contact 3-structure, which we called trans-Sasakian, closely connected with locally conformal quaternionic Kähler manifolds. Finally we give a family of examples of hypercomplex manifolds which are not quaternionic Kähler.},
author = {Cabrera, Francisco Martín},
journal = {Czechoslovak Mathematical Journal},
keywords = {Riemannian manifold; Hermitian manifold; Kähler manifold; almost contact structure; 3-Sasakian structure},
language = {eng},
number = {3},
pages = {545-563},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Almost hyper-Hermitian structures in bundle spaces over manifolds with almost contact $3$-structure},
url = {http://eudml.org/doc/30436},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Cabrera, Francisco Martín
TI - Almost hyper-Hermitian structures in bundle spaces over manifolds with almost contact $3$-structure
JO - Czechoslovak Mathematical Journal
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 3
SP - 545
EP - 563
AB - We consider almost hyper-Hermitian structures on principal fibre bundles with one-dimensional fiber over manifolds with almost contact 3-structure and study relations between the respective structures on the total space and the base. This construction suggests the definition of a new class of almost contact 3-structure, which we called trans-Sasakian, closely connected with locally conformal quaternionic Kähler manifolds. Finally we give a family of examples of hypercomplex manifolds which are not quaternionic Kähler.
LA - eng
KW - Riemannian manifold; Hermitian manifold; Kähler manifold; almost contact structure; 3-Sasakian structure
UR - http://eudml.org/doc/30436
ER -

References

top
  1. Sur les groupes d’holonomie homogène des variétés à connexion affine et des variétés riemanniennes, Bull. Soc. Math. France 83 (1955), 279–330. (1955) MR0079806
  2. Sur les G -structures de type quaternionien, Cahiers de Top. et Geom. Diff. 9 (1967), 389–463. (1967) Zbl0171.20802MR0233302
  3. 10.4310/CAG.1993.v1.n2.a3, Comm. Anal. Geom. 1(2) (1993), 229–279. (1993) MR1243524DOI10.4310/CAG.1993.v1.n2.a3
  4. The geometry and topology of 3 -Sasakian manifolds, J. reine angew. Math. 455 (1994), 18–220. (1994) MR1293878
  5. A classification of almost contact metric structures, Ann. Mat. Pura Appl. (IV) Vol. CLVI (1990), 15–36. (1990) MR1080209
  6. Yang Mills on Riemannian surfaces, Proc. London Math. Soc. 55 (1987), 535–589. (1987) 
  7. 10.2996/kmj/1138846820, Kodai Math. Sem. Rep. 25 (1973), 321–329. (1973) MR0324592DOI10.2996/kmj/1138846820
  8. Quaternion Kählerian manifolds, J. Diff. Geom. 9 (1974), 48–500. (1974) Zbl0297.53014MR0348687
  9. Principal fibre bundles with 1-dimensional toroidal group, Tôhoku Math. J. 2 (1956), 29–45. (1956) MR0080919
  10. Foundations of Differential Geometry, 2 volumes, Intersciences Pub., New York (1963, 1969). (1963, 1969) MR0152974
  11. 10.2996/kmj/1138847001, Kodai Math. Sem. Rep. 26 (1975), 194–200. (1975) MR0377782DOI10.2996/kmj/1138847001
  12. 10.1090/S0002-9947-1966-0192513-X, Trans. Amer. Math. Soc. 122 (1966), 357–367. (1966) Zbl0148.16101MR0192513DOI10.1090/S0002-9947-1966-0192513-X
  13. 10.2748/tmj/1178242759, Tôhoku Math. J. 22 (1970), 325–332. (1970) Zbl0205.25801MR0278225DOI10.2748/tmj/1178242759
  14. 3 -estructuras casi contacto, Tesis Doctoral, Serv. de Public. Univ. de La Laguna (1987). (1987) 
  15. 10.2748/tmj/1178243841, Tôhoku Math. J. 15 (1963), 148–161. (1963) MR0150717DOI10.2748/tmj/1178243841
  16. New classes of almost contact metric structures, Publ. Math. Debrecen 32 (1985), 187–193. (1985) MR0834769
  17. Locally conformal Kähler structures in quaternionic geometric, Trans. Amer. Math. Soc. (1995) (to appear). (ARRAY(0x9064168)) MR1348155
  18. Quaternionic Kähler manifolds, Invent. Math. 67 (1982), 142–171. (1982) Zbl0486.53048MR0664330
  19. 10.1007/BF01446581, Math. Ann. 289 (1991), 421–450. (1991) Zbl0711.53051MR1096180DOI10.1007/BF01446581
  20. Some remarks on quaternion-Hermitian manifolds, preprint, (1994). (1994) 
  21. 10.2969/jmsj/01720167, J. Math. Soc. Japan 17(2) (1965), 167–186. (1965) Zbl0132.16801MR0184166DOI10.2969/jmsj/01720167

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.